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LIBRARY
RONTGEN
THE LLOYD E. HAWES
COLLECTION IN THE
HISTORY OF RADIOLOGY
^Harvard Medical Library
in the Francis A. Countway
Library of Medicine Boston
VERITATEM PER MEDIClXAM QUyERAMUS
Digitized by the Internet Archive
in 2011 with funding from
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http://www.archive.org/details/studyofradiationOOngst
SMITHSONIAN MISCELLANEOUS COLLECTIONS
VOLUME 65. NUMBER 3
Ibobohins jfimb
A STUDY OF THE RADIATION OF THE
ATMOSPHERE
BASED UPON OBSERVATIONS OF THE NOCTURNAL
RADIATION DURING EXPEDITIONS TO
ALGERIA AND TO CALIFORNIA
BY
ANDERS ANGSTROM
(Publication 2354)
CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
1915
Z§e JSorfc (gattimovt fpvtee
BALTIMORE, MD., U. S. A.
PREFACE
The prosecution of the researches described in the following pages
has been rendered possible by several grants from the Hodgkins
Fund of the Smithsonian Institution, Washington, for which I here
desire to express my deep gratitude.
I also stand indebted to various gentlemen for friendly help and
encouragement.
In the first place, I wish to express my sincere thanks to my
esteemed friend, Dr. C. G. Abbot, Director of the Astrophysical
Observatory of the Smithsonian Institution, for the great interest
he has shown in my researches. His aid and suggestions have ever
been a source of stimulation and encouragement, while his criticisms
of my work have never failed to be of the greatest assistance to me.
Other scholars, to whom it is largely due that the observations
upon which this study is based have been so far brought to a success-
ful termination that I have been able to draw from them certain con-
clusions of a general character, are Dr. E. H. Kennard, of Cornell
University ; Professor F. P. Brackett, Professor R. D. Williams, and
Mr. W. Brewster, of Pomona College, California. To all these gentle-
men I wish to express my sense of gratitude and my earnest thanks
for the valuable assistance they have afforded me in my investiga-
tions during the expedition to California.
Ultimately, the value of the observations of nocturnal radiation
here published will be greatly enhanced by the fact that the tempera-
ture, pressure, and humidity of the atmosphere, up to great eleva-
tions, were obtained experimentally by balloon observations made
during the expedition from points at or near my observing stations.
These observations, made by the United States Weather Bureau
in cooperation with the Smithsonian Institution, are given in
Appendix I.
It is also of advantage that observations of the solar constant of
radiation, the atmospheric transparency for solar radiation, and the
total quantity of water vapor in the atmosphere (as obtained by
Fowle's spectroscopic method) were made at Mount Wilson during
the stay of the expedition. A summary of these results forms Ap-
pendix II.
IV PREFACE
In the present discussion the results of the balloon flights and
spectrobolometric work are not incorporated. A more detailed study
of the atmospheric radiation, in which these valuable data would be
indispensable, may be undertaken more profitably after a determina-
tion shall have been made of the individual atmospheric transmission
coefficients throughout the spectrum of long wave rays as depending
on humidity. This study is now in progress by Fowle and others,
and the results of it doubtless will soon be available.
Anders Angstrom.
Upsala, Sweden,
December, ig 14.
CONTENTS
CHAPTER PAGE
Summary I
I. Program and history of the expeditions 3
II. Historical survey 12
III. (a) Theory of the radiation of the atmosphere 18
(b) Distribution of water vapor and temperature in the atmosphere 24
IV. (a) Instruments 28
(b) Errors 31
V. Observations of nocturnal radiation 33
1. Observations at Bassour 33
2. Results of the California expedition 2>7
(a) Influence of temperature upon atmospheric radiation. . 2>7
(b) Observations on the summits of Mount San Antonio,
Mount San Gorgonio, and Mount Whitney, and at Lone
Pine Canyon. Application in regard to the radiation of
a perfectly dry atmosphere and to the radiation of the
upper strata 42
(c) Observations at Indio and at Lone Pine 50
(d) The effective radiation to the sky as a function of time. 52
(e) Influence of clouds 54
VI. Radiation to different parts of the sky 57
VII. Radiation between the sky and the earth in the daytime 70
VIII. Applications to some meteorological problems 76
(a) Nocturnal radiation at various altitudes 76
(b) Influence of haze and atmospheric dust upon the nocturnal
radiation 80
(c) Radiation from large water surfaces 83
Concluding remarks 87
APPENDIX
I. Free-air data in Southern California, July and August, 1913. By
the Aerial Section, U. S. Weather Bureau. Wm. R.
Blair in charge 107
II. Summary of spectrobolometric work on Mount Wilson during Mr.
Angstrom's investigations. By C. G. Abbot 148
III. Some pyrheliometric observations on Mount Whitney. By A. K.
Angstrom and E. H. Kennard 150
A STUDY OF THE RADIATION OF THE ATMOSPHERE
BASED UPON OBSERVATIONS OF THE NOCTURNAL RADIA-
TION DURING EXPEDITIONS TO ALGERIA
AND TO CALIFORNIA
By ANDERS ANGSTROM
SUMMARY
The main results and conclusions that will be found in this paper
are the following. They relate to the radiation emitted by the atmos-
phere to a radiating surface at a lower altitude, and to the loss of
heat of a surface by radiation toward space and toward the atmos-
phere at higher altitudes.
I. The variations of the total temperature radiation of the atmos-
phere are at low altitudes (less than 4,500 m.) principally
caused by variations in temperature and humidity.
II. The total radiation received from the atmosphere is very nearly
proportional to the fourth power of the temperature at
the place of observation.
III. The radiation is dependent on the humidity in such a way that
an increase in the water-vapor content of the atmosphere
will increase its radiation. The dependence of the radi-
ation on the water content has been expressed by an
exponential law.
IV. An increase in the water-vapor pressure will cause a decrease
in the effective radiation from the earth to every point of
the sky. The fractional decrease is much larger for large
zenith angles than for small ones.
V. The total radiation which would be received from a perfectly
dry atmosphere would be about 0.28 — -. — r with a
cm. mm.
temperature of 20°C. at the place of observation.
VI. The radiation of the upper, dry atmosphere would be about
50 per cent of that of a black body at the temperature of
the place of observation.
Smithsonian Miscellaneous Collections, Vol. 65, No. 3.
1
2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
VII. There is no evidence of maxima or minima of atmospheric
radiation during the night that cannot be explained by
the influence of temperature and humidity conditions.
VIII. There are indications that the radiation during the daytime is
subject to the same laws that hold for the radiation during
the night-time.
IX. An increase in altitude causes a decrease or an increase in the
value of the effective radiation of a blackened body
toward the sky, dependent upon the value of the tempera-
ture gradient and of the humidity gradient of the atmos-
phere. At about 3,000 meters altitude of the radiating
body the effective radiation generally has a maximum.
An increase of the humidity or a decrease of the tempera-
ture gradient of the atmosphere tends to shift this maxi-
mum to higher altitudes.
X. The effect of clouds is very variable. Low and dense cloud
banks cut down the outgoing effective radiation of a
blackened surface to about 0.015 calorie per cm.2 per
minute ; in the case of high and thin clouds the radiation
is reduced by only 10 to 20 per cent.
XI. The effect of haze upon the effective radiation to the sky is
almost inappreciable when no clouds or real fog are
formed. Observations in Algeria in 1912 and in Cali-
fornia in 1 91 3 show that the great atmospheric disturb-
ance caused by the eruption of Mount Katmai in Alaska,
in the former year, can only have reduced the nocturnal
radiation by less than 3.0 per cent.
XII. Conclusions are drawn in regard to the radiation from large
water surfaces, and the probability is indicated that this
radiation is almost constant at different temperatures, and
consequently in different latitudes also.
CHAPTER I
PROGRAM AND HISTORY OF THE EXPEDITIONS
It is appropriate to begin this paper with a survey of the external
conditions under which the work upon which the study is based was
done. Most of the observations here given and discussed were
carried out during two expeditions, one to Algeria in 1912, the other
to California in 191 3. An account of these expeditions will give an
idea of the geographical and meteorological conditions under which
the observations are made, and it will at the same time indicate the
program of the field work, a program that was suggested by the
facts referred to in the historical survey of previous work and by
the ideas advanced in the chapter on the theory of atmospheric
radiation.
In 1912 I was invited to join the expedition of the Astrophysical
Observatory of the Smithsonian Institution, led by its Director, Dr.
C. G. Abbot, whose purpose it was to study simultaneously at Algeria
and California the supposed variations of the radiation of the sun.
In May of that year I met Dr. Abbot at Bassour, a little Arab village
situated about 100 miles from Algiers, in the border region between
the Atlas Mountains and the desert, lying at 1,100 meters above sea
level. This place had been selected by Dr. Abbot for the purpose
of his observations on the sun, and on the top of a hill, rising 60
meters above the village, his instruments were mounted under ideal
conditions. The same place was found to be an excellent station
for the author's observations of the nocturnal radiation. A little
house was built of boards by Dr. Abbot and myself on the top of the
hill. This house, about 2 meters in all three dimensions, was at the
same time the living room and the observatory. The apparatus used
for the nocturnal observations was of a type which will be described
in a later chapter. Its principal parts consist of an actinometer, to be
exposed to a sky with a free horizon, a galvanometer, and a milliam-
meter. At Bassour the actinometer was mounted on the roof of
the little observatory, observations of the galvanometer and the
ammeter being taken inside. The horizon was found to be almost
entirely free. In the north some peaks of the Atlas Mountains rose
to not more than half a degree over the horizon, and in the south-
east some few sandy hills screened off with their flat wave-like tops
a very narrow band of the sky.
3
Humidity, mm. Hg.
/
<
m p
oi
fe
Radiation,
cm.' mm.
Humidity, mm. Hg
<
o J?
*? c
2 *
Radiation,
cal.
cm.-* mm.
6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
I was led by several circumstances to think that the nocturnal
radiation to the sky would be found to be a function of the water-
vapor content of the atmosphere and, as a consequence, observations
were made with wet and dry thermometers simultaneously with the
measurements of the radiation. In order not to introduce unneces-
sary influences that might modify this expected effect, it was con-
sidered important always to observe under a perfectly clear sky. It
was found that a few scattered clouds, far from the zenith, seldom
seemed to have any appreciable influence upon the radiation, but, in
order not to introduce conditions of the effect of which one could
not be quite sure, all the observations made at Bassour and used in
this paper were made under a perfectly cloud-free sky. The climatic
conditions were favorable for this program, and observations were
taken almost every night under a clear sky. Observations were also
made of the radiation to different parts of the sky, this study being
considered as of special interest in connection with the general
problem.
It was my purpose also to make an investigation of the influence
of altitude upon the radiation to the sky, and in fact some prelimi-
nary measurements were carried out with a view to the investigation
of that problem. Thus I made observations one night in the valley
of Mouzaia les Mines, situated at the foot of the peak of Mouzaia
among the Atlas Mountains, about 15 miles from Bassour. The
height of the valley above sea level is 540 meters. Simultaneously
Dr. Abbot observed at Bassour (1,160 m.) on this particular night,
as well as during the following one, when I took measurements on
the top of Mouzaia (1,610 m.). The result of these observations
will be found among the investigations of the California expedition,
one of the purposes of which was to consider more closely the
problem of the influence of altitude upon the radiation of the atmos-
phere. For assistance with the practical arrangements in connection
with the expedition to Mouzaia my hearty thanks are due to M. de
Tonnac and M. Raymond, property owners.
As the most important result of the observations in Algeria it
was found that the water vapor exerted a very marked influence
upon the nocturnal radiation to the sky ; a change in the water- vapor
pressure from 12 to 4 mm., causing an increase in the nocturnal
radiation amounting to about 35 per cent, other conditions being
equal. From the observations it was possible to arrive at a logically
founded mathematical expression for this influence.
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM J
A further investigation of the problem seemed, however, neces-
sary. My special attention was directed to the influence of altitude
and the influence of the temperature conditions of the instrument
and of the atmosphere upon the radiation to the sky. For this
purpose the climatic and geographic conditions of California were
recommended as being suitable by Dr. Abbot.
There is probably no country in the world where such great dif-
ferences in altitude are found so near one another as in Cali-
fornia. Not far from Yosemite Valley, in the mountain range of
Sierra Nevada, the highest peak in the United States, Mount Whit-
ney, raises its ragged top to 4,420 meters, and from there one can
look down into the lowest country in the world, the so-called
Death Valley — 200 meters below sea level. And further south, near
the Mexican frontier, there is the desert of the Salton Sea, of which
the lowest parts are below sea level; a desert guarded by mountain
ranges whose highest peaks attain about 3,500 meters in altitude.
In the summer the sky is almost always clear ; a month and more may
pass without a cloud being visible. It was evident that the geographi-
cal as well as the meteorological conditions of the country were very
favorable for the investigations I contemplated.
On the advice of Dr. Abbot, ^therefore drew up a detailed plan
for an expedition to California, which was submitted to the Smith-
sonian Institution, together with an application for a grant from
the Hodgkins Fund. The application was granted by the Institution,
to whose distinguished secretary, Dr. Charles D. Walcott, I am much
indebted for his great interest in the undertaking. The program for
the expedition was as follows :
1. Preliminary observations at the top of Mount San Antonio
(3,000 m.) and at Claremont (125 m.) simultaneously (3 nights).
2. Simultaneous observations at the top of Mount San Gorgonio
(3,500 m.) and at Indio in the Salton Sea Desert (o m.), (3 nights).
3. Expedition to Mount Whitney. Here the observations were to
be extended to three stations at different altitudes, where simultane-
ous measurements should be made every clear night during a period
of about two weeks. The stations proposed were : Lone Pine, at
the foot of the mountain, at 1,200 m. altitude ; the summit of Mount
Whitney (4,420 m.) ; and an intermediate station on one of the
lower ridges that project on the eastern side of the mountain. Dur-
ing this part of the expedition, as well as during the preliminary
ones, , the observations were to be made once an hour during the
entire night, from 8 o'clock in the evening to 4 o'clock in the morn-
8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 6$
ing. It was proposed also to make pyrheliometric observations dur-
ing the days on the top of Mount Whitney. These latter measure-
ments, which are taken as a basis for determinations of the solar
constant are given in an appendix written by Dr. Kennard and
myself.1
The Mount Whitney part of the expedition was regarded as by
far the most important, both on account of the higher altitude of the
station, and because of the conveniences presented by the position
on the top of the mountain, which made it possible to observe there
during a considerable interval of time. Mount Whitney is too well
known through the expedition of Langley (in 1881) and of Abbot
(in 1909 and 1910) to need any description here. In the year 1909,
the Smithsonian Institution erected — on the suggestion of Directors
Campbell and Abbot — a small stone house on the summit as a shelter
for future observers. Permission was given me by the Smithsonian
Institution to use this shelter for the purposes of the expedition.
As the observations were to be made simultaneously in different
places, several observers were needed. At this time (in the begin-
ning of the year 1913) I was engaged in some investigations at the
physical laboratory of Cornell University, Ithaca, N. Y., and from
there I was enabled to secure the services of my friend, Dr. E. H.
Kennard, as a companion and an able assistant in the work of the
expedition. Further, Prof. F. P. Brackett, Director of the Astro-
nomical Observatory of Pomona College, Claremont, California,
promised his assistance, as also did Professor Williams and Mr.
Brewster from the same college.
On the 8th of July, 191 3, the author and Dr. Kennard arrived
at Claremont, California, where Messrs. Brackett, Williams, and
Brewster joined us. Through the kindness of Prof. Brackett the
excellent little observatory of Pomona College was placed at my
disposal as headquarters, and here the assistants were instructed,
and the instruments — galvanometers, actinometers and ammeters —
were tested.
On the 12th of July the first preliminary expedition was made,
when the author and Mr. Brewster climbed to the summit of
Mount San Antonio, the highest peak of the Sierra Madre Range
(3,000 m.) and observed there during the two following nights.
At the same time Prof. Brackett and Dr. Kennard observed at
Claremont at the foot of the mountain, but unfortunately at the
1 This paper has also appeared in the Astrophysical Journal, Vol. 39, No. 4,
May, 1914.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 9
lower station the sky was cloudy almost the entire time, which con-
dition, however, furnished an opportunity to demonstrate the effect
of dense homogeneous cloud banks upon the nocturnal radiation.
The first simultaneous observations at different altitudes, favored
by a clear sky at both stations, were obtained during a subsequent
expedition, also of a preliminary nature, when the author and
Mr. Brewster, proceeded to Indio in the Salton Sea Desert, and
Prof. Brackett, Prof. Williams, and Dr. Kennard succeeded in climb-
ing Mount San Gorgonio (3,500 m.), the highest peak of the San
Bernardino range. Indio was chosen because of its low altitude
(o m.) and because of its meteorological conditions, the sky being
almost always clear in this part of the desert. The horizon was
almost perfectly free, the San Bernardino and San Jacinto moun-
tains rising only to about io° above the horizon. The temperature
at the lower station, which is situated in one of the hottest regions of
America, reached, in the middle of the day, a point between 400 and
46 ° C. ; in the night-time it fell slowly from about 30 ° in the evening
to about 200 in the morning. Here some interesting observations
were obtained, showing the influence of temperature upon radiation
to the sky. At the same time, the other party made observations on
the top of Mount San Gorgonio (3,500 m.) situated about 40 miles
farther north. The party climbed to the top in a heavy snow-
storm, and during the two following, perfectly clear, nights, observa-
tions were taken, the temperature at the top being about o° C. Thus
simultaneous observations were obtained on two places differing
in altitude by 3,500 meters.
The expedition to Mount Whitney, for which preparations were
made immediately after the return of the parties to Claremont, was
regarded as the most important part of the field work. On the pro-
posal of Director Abbot, the U. S. Weather Bureau had resolved to
cooperate with my expedition in this part of the undertaking. Under
the direction of Mr. Gregg and Mr. Hathaway of that Bureau, the
upper air was to be explored by means of captive balloons, carrying
self-recording meteorological instruments. In this way the tempera-
ture and the humidity would be ascertained up to about 1,500 meters
above the point from which the balloons were sent up. The ascents
were to be made from Lone Pine (by Mr. Hathaway) and from
the summit of Mount Whitney (by Mr. Gregg). The latter ascents
are probably the first that have been carried on by means of captive
balloons at altitudes exceeding 4,000 meters.
10 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
On July 29 the party, accompanied by Mr. Gregg and Mr. Hatha-
way of the Weather Bureau, left Los Angeles for Lone Pine, Inyo
County, California. After arrival there in the morning a suitable
place was found for the lower station, and final arrangements were
made for the guide and pack train for the mountain party. The
disposition of the observers was to be Angstrom and Kennard at the
upper station, Brewster and an assistant at the intermediate station,
where observations were to be made only in the mornings and even-
ings, and, finally, Williams and Brackett at the lower station.
On Thursday, July 31, the mountain party set out from Lone Pine
with Elder, the Mexican guide, a cook, a pack train of seven mules,
and a light cart to convey the party up the incline to the foot of
Lone Pine Canyon, whence the ascent would have to be made on foot
or in the saddle. After some prospecting on the way, the inter-
mediate station was located on a crag overlooking the canyon from a
precipitous height of several hundred feet. Here Brewster was
stationed and was later joined by a Mexican helper. Leaving Brew-
ster, the party climbed that night to Elder's camp, at an elevation
of nearly 3,000 meters. In spite of a storm which began with rain in
the night and changed to snow, increasing in severity the next day, the
summit was reached early in the afternoon. A thrilling electric
storm raged for some time. Every point of rock and the tips of the
nails and hair emitted electric discharges. But the little stone-and-
iron building of the Smithsonian Institution furnished shelter. That
the climbing of the mountain, with many instruments and a large
pack train, succeeded without an accident, is largely due to the
excellent work of Mr. G. F. Marsh, of Lone Pine, who had worked
for weeks with a gang of 20 men to open up the trail, so that the
ascent might be possible for men and pack animals carrying pro-
visions, instruments, and fuel. Even so, in its upper reaches the
trail passes over long slopes of ice and snow and clings to the face
of naked and rugged steeps, where a false step would be fatal.
On the top of the mountain, a short distance from the house, is
a little flat-roofed stone shelter about six feet square and eight feet
high. In and upon this shed most of the instruments were set up.
On the whole, the weather upon the mountain was very favorable
for the work of the expedition. Observations were made on seven
nights out of a possible ten. Besides the hourly records of nocturnal
radiation, the solar radiation was measured at suitable intervals
throughout the day, and complete records were kept of the tempera-
ture, humidity, and pressure of the air at the summit. Strong winds
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM II
interfered with the balloon ascents, but several of them were suc-
cessful. During three nights records were obtained up to 400 to
1,000 meters above the station.
The observations at the lower stations have also proved to be very
satisfactory. In the section on the experimental work the observa-
tions will be discussed in detail.
CHAPTER II
HISTORICAL SURVEY1
Insolation from the sun, on the one hand, and, on the other, radia-
tion out to space, are the two principal factors that determine the
temperature conditions of the earth, inclusive of the atmospheric
envelope. If we do not consider the whole system, but only a volume
element within the atmosphere (for instance, a part of the earth's
surface) this element will gain heat: (I) through direct radiation
from the sun; (II) from the portion of the solar radiation that is
diffused by the atmosphere ; (III) through the temperature radiation
of the atmosphere. The element will lose heat through temperature
radiation out to space, and it will lose or gain heat through convection
and conduction. In addition to these processes, there will often occur
the heat transference due to the change of state of water : evapo-
ration, condensation, melting, and freezing. The temperature radi-
ation from the element to space, diminished by the temperature
radiation to it from the atmosphere, is often termed " nocturnal
radiation," a name that is suggested by the fact that it has generally
been observed at night, when the diffused skylight causes no compli-
cation. In this paper it will often be termed " effective radiation."
The effective radiation out to the sky together with the processes of
convection and conduction evidently under constant conditions must
balance the incoming radiation from sun and sky. The problem of
the radiation from earth to space is therefore comparable in impor-
tance to the insolation problem in determining the climatic conditions
at a certain place.
The first observations relating to the problem of the earth's radia-
tion to space are due to the investigations of Wilson,2 Wells,3 Six,4
Pouillet,5 and Melloni,6 the observations having been made between
the years 1780 and 1850. These observers have investigated the
1 Large parts of this chapter as well as of chapters III, IV and V : 1 have
appeared in the Astrophysical Journal, Vol. 37, No. 5, June, 1913.
2 Edinburgh Phil. Trans., Vol. 1, p. 153.
3 Ann. de chimie et de physique, tome 5, p. 183, 1817.
4 Six, Posthumous Works, Canterbury, 1794.
5 Pouillet, Element de physique, p. 610, 1844.
8 Ann. de chimie et de physique, ser. 3, tome 22, pp. 129, 467, 1848.
Ibid., ser. 3, tome 21, p. 145, 1848.
12
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 1 3
nocturnal cooling of bodies exposed to the sky, a cooling that is
evidently not only due to radiation but is also influenced by conduc-
tion and convection of heat through the surrounding medium.
Melloni, making experiments in a valley called La Lava, situated
between Naples and Palermo, found that a blackened thermometer
exposed on clear nights showed a considerably lower value (3.60 C.)
than an unblackened one under the same conditions. Melloni draws
from his experiments the conclusion that this cooling is for the most
part due to the radiation of heat to space. In fact, such a cooling
of exposed bodies below the temperature of their surroundings was
very early observed. Natives of India use it for making ice by ex-
posing flat plates of water, on which dry grass and branches are
floating, to the night-sky. The formation of ice, due to nocturnal
radiation, has been systematically studied by Christiansen.
So far the observations have been qualitative rather than quantita-
tive and the object of the observations not clearly defined. The first
attempt to measure the nocturnal radiation was made by Maurer,
the Swiss meteorologist. In the year 1886, Maurer published a
paper dealing with the cooling and radiation of the atmosphere.1
From thermometrical observations of the atmosphere's cooling he
deduces a value S = 0.007. io-4 (cm.3 min.) for the radiation coefficient
of the air and- from this a value for the radiation of the whole atmos-
phere : 0.39 7T-—- — at o°. This value is obtained on the assump-
cm.- mm.
tion that the atmosphere is homog-eneous, having a height of 8.105
cm. and by the employment of the formula
R=S.[i-e-an]
a
where 5" is the radiation, a the absorption coefficient and /i = 8.io5.
Maurer's manner of proceeding in obtaining this value can scarcely
be regarded as quite free from objection, and in the theoretical part
of this paper I shall recur to that subject. But through his theory
Maurer was led to consider the problem of the nocturnal radiation
and to measure it.2 His instrument consisted of a circular copper
disk, fastened horizontally in a vertical cylinder with double walls,
between which was running water to keep the cylinder at a constant
temperature. The cover of the cylinder was provided with a cir-
cular diaphragm, which could be opened or shut. Opening and
shutting this diaphragm at certain intervals of time, Maurer could,
1 Meteorologische Zeitschrift, 1887, p. 189.
2 Sitzber. der Ak. der Wissensch. zu Berlin, 1887, p. 925.
14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
from the temperature of the disk read on a thermometer, compute
the radiation. He made his observations at Zurich during some
clear nights in June and found a nocturnal radiation amounting to
0.13 cal. By this method, as well as by the similar method used by
Pernter, certain corrections must be made for conduction and con-
vection, and certain hypotheses must be made in order to compute
the radiation to the whole sky from the radiation to a limited part of
it given by the instrument.
The observations of Pernter ' were made simultaneously on the
top of Sonnblick (3,095 m.) and at Rauris (900 m.). He observed
with an actinometer of the Violle type and found a radiation of 0.201
cal. (unless otherwise stated the radiation is always given as
C9.1
— '—. — in this paper) at the higher station and 0.1^1 at the lower
cm.2 mm. r r J to J
one.
Generally the methods for determining the effective radiation out
to space have proceeded parallel — with a certain phase difference —
with the development of the methods of pyrheliometry. In the year
1897, Homen2 published an important paper bearing the title " Der
tagliche Warmeumsatz im Boden und die Warmestrahlung zwischen
Himmel und Erde." His method was an application of a method
employed by K. Angstrom for measuring sun radiation. The prin-
cipal part of the instrument consists of two exactly equal copper
plates. In the plates are introduced the junctions of a thermocouple.
If now one of the plates is exposed to the radiation and the other
covered, there will be a temperature difference between the disks
growing with the time. If at a certain temperature difference, S,
the conditions are interchanged between the disks, they after a
certain time, t, will get the same temperature. Then the intensity
of the radiation is given by the simple formula :
t
where W is the heat-capacity of the disks. By this method the
effects of conduction and convection are eliminated. The weak
point of the instrument, if applied to measurements of the nocturnal
radiation, lies in the employment of a screen, which must itself
radiate and cool, giving rise to a difference in the conditions of the
two disks. Homen draws from his observations on the radiation
between earth and sky the following conclusions :
Sitzber. der Ak. der Wissensch. zu Wien, 1888, p. 1562.
Homen, Der tagliche Warmeumsatz, etc., Leipzig, 1897
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM I 5
(i) If the sky is clear, there will always be a positive radiation
from earth to sky, even in the middle of the day.
(2) If the sky is cloudy, there will always, in the daytime, be a
radiation from sky to earth.
(3) In the night-time the radiation for a clear as well as for a
cloudy sky always has the direction from earth to sky.
Horaen also made some measurements of the radiation to different
parts of the sky and found that this radiation decreases rapidly when
the zenith angle approaches the value 900. His values of the noc-
turnal radiation vary between 0.13 and 0.22 for a clear sky.
When relatively large quantities of heat are to be measured under
circumstances where the conduction and convection are subject to
considerable variation, it is favorable if one can apply a zero method,
where the instrument is kept the whole time at the temperature of its
surroundings. As the first attempt to discover such a method may be
regarded the experiment of Christiansen, who measured the thick-
ness of ice formed on metal disks that were placed on a water-surface
and exposed to the sky. In 1899 K. Angstrom published a descrip-
tion of the compensation pyrheliometer and shortly afterward ( 1903)
a modified type of this instrument was used by Exner 1 in order to
measure the nocturnal radiation on the top of Sonnblick. In agree-
ment with former investigations made by Maurer and Horaen, Exner
found the radiation to be relatively constant during the night. He
points out that there are tendencies to a slight maximum of radiation
in the morning, one to two hours before sunrise. To the method
of Exner it can be objected that the radiation is only measured for
a part of the sky. In order to obtain the radiation to the whole sky,
Exner applied a correction with regard to the distribution of
radiation to the different zones given by Homen. It will be shown
in a later part of this paper that such a procedure is not entirely
reliable.
In 1905 K. Angstrom2 gave a description of an instrument
specially constructed for measuring the nocturnal radiation. The
instrument is founded upon the principle of electric compensation,
and, as it has been used in the work here published, I shall in a
following chapter give a more detailed consideration of it. With this
instrument Angstrom measured the nocturnal radiation during sev-
eral nights at Upsala and found values varying between 0.13 and
1 Met. Zt., 1903, p. 409.
2 Nova Acta Reg. Soc, Sc. Upsal., Ser. 4, Vol. 1, No. 2.
i6
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
0.18 cal. for a clear sky. With this type of instrument Lo Surdo 1 has
made measurements at Naples. He observed the radiation during
a clear and especially favorable night and found a pronounced maxi-
mum about two hours before sunrise. Contrary to Homen he finds
a positive access of radiation from the sky even when the sky is
clear. The following table gives a brief survey of the results ob-
tained by different observers :
Observer
Date
Maurer June 13-18, 1887
Pernter Feb. 29, 1888
Pernter Feb. 29, 1888
Homen Aug., 1896
Exner 1902
Exner July 1, 1902
K.Angstrom May-Nov., 1904
Lo„Surdo... Sept. 5-6, 1908
July I,
May-Nov.,
Sept. 5-6,
A. Angstrom July 10-Sept. 10
1912
Place
Temperature Height Mean Value
Zurich
Sonnblick
Rauris
Lojo'see
Sonnblick
Sonnblick
Upsala
Naples
Algeria
15°-"
0-10°
20°-30°
20°
500
3095
900
3J.06
3106
200
30
1 160
0.128
0.201
0.I5I
0. 17
0. 19
0.268 (max.)
0.155
0. 182
0.174
If we apply the constant of Kurlbaum a = 7. 68.1 o-11, to the law of
Stefan-Boltzmann for the radiation of a black surface, we shall find
that such a surface at 15 ° C. temperature ought to radiate 0.526 cal.
If the observed effective radiation does not amount to more, for in-
stance, than 0.15 cal.,. this must depend upon the fact that 0.376 cal.
is radiated to the surface from some other source of radiation. In
the case of the earth this other source of radiation is probably to a
large extent its own atmosphere, and in the following pages we shall
often for the sake of convenience discuss this incoming radiation
as if it were due to the atmosphere, ignoring the fact that a small
fraction of it is due to the stars and planetary bodies.
Then the source of variations in the effective radiation to the sky
is a double one. The variations depend upon the state of the radiat-
ing surface and also upon the state of the atmosphere. And the state
of the atmosphere is dependent upon its temperature, its composition/
density, the partial and total pressure of the components, and upon
the presence of clouds, smoke, and dust from various sources.
The present paper is an attempt to show how the effective radia-
tion, and consequently also what we have defined as the radiation
of the atmosphere, is dependent upon various conditions of the
atmosphere. It must be acknowledged that the conditions of the
atmosphere are generally known only at the place of observation.
1 Nuovo Cimento, Ser. 5, Vol. 15, ic
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM I1/
But it has been shown by many elaborate investigations that, on
an average, we are able, with a certain amount of accuracy, to draw
conclusions about a large part of the atmosphere from observations
on a limited part of it. This will be further discussed in a chapter
on the distribution of water vapor and temperature conditions. The
discussion of the observations will therefore be founded upon mean
values, and will lead to a knowledge of average conditions.
CHAPTER III
A. THEORY OF THE RADIATION OF THE ATMOSPHERE
The outgoing effective radiation of a blackened body in the night
must be regarded as the sum of several terms : (i) the radiation from
the surface toward space (Ec) given, for a " black body," by Stefan's
radiation law ; (2) the radiation from the atmosphere to the surface
(Ea), to which must be added the sum of the radiations from sidereal
bodies (Es), a radiation source that is indicated by Poisson by the
term " sidereal heat." If / is the effective radiation, we shall evi-
dently have :
J =z JC-c t-'d, EL&
For the special case where the temperature of the surface is con-
stant and the same is assumed to be the case for the sidereal radiation,
we can write :
J = K-Ea
K being a constant. Under these circumstances the variations in the
effective radiation are dependent upon the atmospheric radiation
only, and the problem is identical with the problem of the radiation
from a gaseous body, which in this case is a mixture of several
different components. As is well known from thorough investiga-
tions, a gaseous body has no continuous spectrum, but is charac-
terized by a selective radiation that is relatively strong at certain
points of the spectrum and often inappreciable at intermediate
points. The law for the distribution of energy is generally very
complicated and is different for different gases. The intensity is
further dependent upon the thickness, density, and temperature of
the radiating layer.
Let us consider the intensity of the radiation for a special wave
length A, from a uniform gaseous layer of a thickness R and a tem-
perature T toward a small elementary surface dr. To begin with,
we will consider only the radiation that comes in from an elementary
radiation cone, perpendicular to dr, which at unit distance from dr
has a cross-section equal to da. One can easily deduce :
[R
Jx= exe~a\r drdQdr
which sfives for unit surface :
Jx=e-±.dn(i-e-a\R) (1)
18
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM IO,
where e\ is the emission coefficient and a\ the absorption coefficient
for the wave length A.
Evidently :
Urn Jx=~dn = ExdCl . (2)
R=oo a\
where E\ is the radiation from a black body for the wave length
A at the temperature T. It follows from this that, in all cases where
one can assume ax to be independent of the temperature, ex must
be the same function of the temperature as E\ multiplied by a con-
stant. That means that the radiation law of Planck must always
hold, as long as the absorption is constant :
ex = CA-5 1
e\T -1
If now the gas has many selective absorption bands we may write
instead of (i) :
J=2Ex(i-e-a\R)d€l (3)
With the aid of (3) it is always possible to calculate the radiation
for any temperature, if the absorption coefficient, which is assumed
to be constant, is known.
If R is taken so great that the product a\ ■ R has a very large
value for all wave lengths, the expression (3) will become
lim J = %Ex = uTi (4)
axR=oo
which is Stefan's radiation law for a black body.
If axR cannot be regarded as infinitely great for all wave lengths,
the radiation, J, will be a more complicated function of T expressed
by the general relation (3). The less the difference is between the
radiation from the gas and the radiation from a black body at the
same temperature, so much more accurately will the formula (4)
express the relation between radiation and temperature.
Dr. Trabert1 draws from observations on the nocturnal cooling
of the atmosphere the conclusion that the radiation from unit mass
of air is simply proportional to the absolute temperature. If this
should be true, it can be explained only through a great variation
of ax for a variation in the temperature. Later Paschen2 and Very8
measured in the laboratory the radiation from air-layers at different
1 Denkschriften der Wien. Akad., 59.
2 Wied. Ann., 50, 1893.
3 Very, Atmospheric Radiation, Washington, 1900.
20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
temperatures and found a much more rapid increase with rising
temperature than that indicated by Trabert.
From (3) we shall deduce some general laws for the radiation
from gaseous layers. From such a layer the radiation will naturally
come in from all* sides, R being different for different angles of
incidence. We may therefore write (3) in the form:
j = "izEx(i-e-*\-yK) (5)
where y is always a positive quantity. Xow we have :
That is, we have the very evident result that the radiation of
a gaseous layer increases with its thickness (or density). For very
thick layers the increase is zero and the radiation constant.
By a second differentiation we get :
d2J ^x
aJr2 = -%%{ax.yye-^y*
The second derivative is always negative, which shows that the
curve giving the relation between radiation and thickness is alzvays
concave tozvard the R-axis.
We may now go a step further and imagine that on the top of
the first layer is a new layer, which radiates in a certain way different
from that of the first layer. A part of the radiation from the second
layer will pass the first layer without being absorbed. That part we
denote by H. Another fraction of the radiation will be absorbed, and
it will be absorbed exactly at the wave lengths where the first layer
is itself radiating. The sum of the radiations from the two layers
can therefore be expressed by a generalization of (5)
j = H + iz[Ex-(Ex-E'x)e-a\-vR] (6)
where E\ is the radiation from the second layer at the wave length
A. If this layer has the same or a lower temperature than the first
one, we evidently have :
E\<EX
In that case the laws given above in regard to the derivatives of
/ evidently hold, and we find here also that the less the thickness of
the layer is, so much more rapid is the increase of radiating pozver
with increase in thickness. This is true for a combination of several
layers under the condition that the temperature is constant or is a
decreasing function of the distance from the surface to which the
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 21
radiation is measured. We shall make use of that fact in the experi-
mental part of this paper, in order to calculate the maximum value
of the radiation of the atmosphere when the density of one of its
components approaches zero.
The relation
represents the general expression for the radiation within the radia-
tion cone dQ, perpendicular to the unit of surface. Maurer bases his
computation of the atmosphere's radiation upon the more simple
expression
/ = i-(i-^*R)
a
where he puts R equal to the height of the reduced atmosphere and
a equal to the absorption coefficient of unit volume. This is evidently
an approximation that is open to criticism. In the first place it is
not permissible to regard R as the height of the reduced atmosphere,
and this for two reasons : first, because the radiation is chiefly due to
the existence of water vapor and carbon dioxide in the atmosphere
vapors, whose density decreases rapidly with increase in the altitude ;
and, secondly, because we have here to deal with a radiation that
enters from all sides, R being variable with the zenith angle. But even
if we assign to R a mean value with regard to these conditions,
Maurer's formula will be true only for the case of one single emission
band and is, for more complicated cases, incapable of representing
the real conditions. I have referred to this case because it shows
how extremely complicated are the conditions when all are taken into
consideration.
If, with Maurer, we regard the atmosphere as homogeneous and
of uniform temperature, having a certain height, h, we must, con-
sidering that R is a function of the zenith angle, write (i) in the
following form:
/x= MrfQ ( i - *Ta* • c^iO cos * (7)
a\J
where the integration is to be taken over the hemisphere represent-
ing the space. Now we have
d£l = d&dif/ sin <3>
and therefore
r ""
7X=-^- |#r (j-e-^-^h) sin*cos$cte (8)
a\ Jo Jo
22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
This expression can easily be transformed into :
JK = 7rEx(l-2^re~* (l.Y) (9)
Jp X"
where p = a\- h and x = a.. -. When h = o, this expression ap-
A cos <£
proaches zero; when h==co, J\ approaches the value ttE\, which is
equal to the radiation of a black body under the same conditions. We
have, in fact :
c~p
/•co r 3 p — p
lim p- — — dx— lim = lim =o
p = go Jp ■* p = cox -1 p = 00 — '
2 p3
and in a similar way :
lim p-
p=0
— rf -— —
xz ' ~ 2
We shall now consider in what respects these relations are likely
to be true for the very complicated conditions prevailing- in the
atmosphere. The atmosphere, considered in regard to its radiating
properties, consists of a low radiating layer up to about 10 km. made
up of water vapor and carbon dioxide, and a higher radiating layer
composed of carbon dioxide and ozone. These two layers naturally
merge into one another, but it is convenient here to suppose a clear
distinction, our surface of separation being at the altitude where the
water vapor ceases to have any appreciable influence upon the
radiation of the atmosphere.
The radiation of the lower layer is chiefly dependent upon the
amount of water vapor contained in it, the strong radiation of the
carbon dioxide being at wave lengths where the water vapor itself
must radiate almost in the same way as a black body. At any rate,
the variations of the radiation in that part of the atmosphere must
depend almost entirely on the variations in the water-vapor element,
the carbon-dioxide element being almost constant, as well in regard to
time, as to place and to altitude. The probable slight influence of vari-
ations in the amount of ozone contained in the upper strata of the
atmosphere, we may at present ignore. Including the constant
radiation of the carbon dioxide in the radiation of the upper layer,
we can apply the expression (5) and arrive at
J = H + i$[Ex-(Ex-E\)e-"\-vK-] (10)
where R can be put equal to the height of the reduced water-
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 27,
vapor atmosphere, or, what is the same, the amount of water vapor
contained in a vertical cylinder of I cm.2 cross-section. Here a\
has been considered as a constant. As has been shown by Miss von
Bahr, the law of Beer does not, however, hold for vapors, absorption
being variable with the total pressure to which the vapor is subjected.
As will be seen in the experimental part of the paper, this circum-
stance has probably introduced a slight deviation from the conditions
to be expected from the assumption of a constant value for a.
From (10) we draw a similar conclusion to the preceding: with
decreasing water-vapor content, the radiation of the atmosphere will
also decrease and this decrease will be more rapid at a low water-
vapor content than at a high one.
The simplest form in which (10) can be written is obtained from
the assumption that we can put :
and
22 ( Ex - E\ ) e~aWR = Ce~am ymR = CW
where P is the height of the reduced water-vapor atmosphere. In
such a case we shall obtain for the radiation of the atmosphere:
Ea=K-Ce-V (ii)
and for the effective radiation :
J=E' + Ce-ep (12)
We have heretofore supposed that the temperature of the radiating
layer is constant. If that is not the case, it will introduce a new
cause of variations. For every special wave length the radiation
law of Planck will hold, but the integration will generally give a
result different from the law of Stefan, dependent upon the different
intensities of the various wave lengths relative to those of a black
body. From the measurements of Rubens and Aschkinass on the
transmission it can be seen, as will be shown later, that the radiation
of the water vapor is very nearly proportional to the fourth power
of the temperature, and as an approximation one may write :
Ea=<rTiF{P)
or for the simple case ( 1 1 ) :
Ea = cT*(K"-e-P?)
Use will be made of these considerations in the treatment of the
observations made.
24 SMITHSONIAN .MISCELLANEOUS COLLECTIONS VOL. 65
B. DISTRIBUTION OF WATER VAPOR IN THE ATMOSPHERE1
In applying observations of the effective radiation toward the sky-
to determine a relation between the radiation of the atmosphere and
its temperature and humidity, we are met by two great difficulties :
First, the measurement of the total quantity of water contained in
the atmosphere (I shall call this quantity hereafter the "integral
water vapor " of the atmosphere) ; second, the determination of the
effective atmospheric temperature.
There have been several elaborate investigations made of the water
component of the atmosphere, by humidity measurements from
balloons and on mountains, and indirectly by observations of the
absorption, resulting from the water vapor, in the sun's radiation.
Hann 2 has given the following formula, applicable to mountains, by
which the water-vapor pressure at any altitude can be expressed as
a function of the water-vapor pressure e observed at the ground.
If e0 is the observed water-vapor pressure in millimeters of mercury
at a certain place, and h the altitude in meters above this place, the
vapor pressure en at the height h meters is
: ene 2730
(1)
In the free air the decrease of the pressure with altitude is more
rapid, especially at high altitudes. From observations in balloons,
Suring has given the formula : 3
eh = e0e 2606\ T 20/ ^ ■>
If the atmosphere has the same temperature all through, the water
element contained in a unit volume will be proportional to the vapor
pressure. It is easy to see from the expression of Hann or of Suring
that in such a case the integral water vapor will be proportional to the
vapor pressure at the earth's surface. Through integration we shall
get from Hann's formula :
F = 2-73fo • 103 (3)
and from Siiring's formula :
^ = 2.I3/0-IO3 (4)
where /0 is the water content in grams per cm.3 at the earth's surface.
1 See the concluding part of the preface. The discussion here given is for
the purpose of indicating how far observations of humidity and temperature
at the earth's surface may take the place of detailed information obtainable
only by balloon flights in the study of atmospheric radiation.
2 Hann, Meteorologie, pp. 224-226.
3 Arrhenius, Lehrbuch der Kosmischen Physik, p. 624.
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 25
When one wishes to compute the integral water vapor from the
pressure, the fall of temperature will cause a complication. From
(1) we get, instead of (3) :
- _A_
Th • fh = T0f0e 2730
where Th denotes the absolute temperature at the altitude h meters.
Th is a function of the altitude. This function differs from time to
time and can be known only by balloon observations, but for present
purposes we may use an approximate formula for Th. We may write,
Th is equal to T0 when h = o and Th is equal to o° at h = 00 . Also,
we must have — =0 at /{ = 00. Accordingly (as the temperature
ah
influence in the formula is not great) it may suffice to assume that
T on an average can be expressed by an exponential function of the
form:
Th=T0e~ah (6)
AT
where a is to be determined by assuming that for h = o -—- is
ah
equal to the observed fall of temperature at the surface of the
earth. For a fall of temperature of 0.7 degree per 100 m. one finds
a = 0.03. Introducing (3) into (1) we obtain the slightly different
result for the integral water vapor :
F = 2.94-/0- io3
and in a similar way from Suring's formula :
Hann's formula, which holds for mountain regions, indicates that
here the element of water vapor contained in the atmosphere above
a certain place is the absolute humidity at that place multiplied by
a constant, the constant being independent of the altitude. This
is not the case for the free air, if Suring's formula may be taken as
a true expression of the conditions here prevailing. It is true that at
a certain place we shall have F=cf0, c being a constant, but this
constant will differ at different altitudes. At an altitude of 4,400 m.,
we shall have
F= 1 .8 • /4,400 ( free air)
Fowle has made an interesting study of the absorption pro-
duced by water vapor in the sun's energy spectrum at Mount Wil-
son.1 He also finds that the amount of water vapor contained in
lAstrop. J., 2,7, N. 5, p. 359.
26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the air is proportional to f0 under average conditions. Individual
observations deviate, however, greatly from the computed value,
which is to be expected in view of the variety of atmospheric con-
ditions.
Briefly it may be said that the observations agree in showing that
on an average the integral water vapor above a certain place is pro-
portional to the absolute humidity at that place. The factor of pro-
portionality is, however, in general a function of the altitude.
The application of these results to the present question means that
we can replace the water content of the whole atmosphere (P) by
the absolute humidity at the place of observation multiplied by
a constant, the latter being a quantity it is possible to observe.
For the general case we thus obtain
or for the simplest possible case
Ea=K-Ce-vf°
More difficult is the problem of assigning a mean value for the
temperature of the radiating atmosphere. It is evident that this
temperature is lower than the temperature at the place of observa-
tion, and it is evident that it must be a function of the radiating
power of the atmosphere. The most logical way to solve the problem
would be to write T as a function of the altitude and apply Planck's
law to every single wave length. The radiation of the atmosphere
would thus be obtained as a function of the humidity and the tem-
perature ; but even after many approximations the expression would
be very complicated and difficult to test. The practical side of the
question is to find out through observations how the radiation
depends upon the temperature at the place of observation. Suppose
this temperature to be T0. We may consider a number of layers
parallel with the surface of the earth, whose temperatures are
7\, To, T3, etc. Suppose, that these layers radiate as the same function
cTna of the temperature. Let us write: T1 = mT0: T2=nT0;
T3 = qT0. Then the radiation of all the layers will be :
J-cT0a- [ama + pna + yqa ]
at another temperature t0 the radiation will be :
i=Ct0a- [amf + pilf + yqf ]
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 2.J
The condition that the whole layer shall radiate proportionally to
this function cT0a, is evidently that we have :
iu = m1 ; n=n1 ; q = qx. . . .
that is : The temperature at every altitude ought to be proportional
to the temperature at the zero surface. This is approximately true
for the atmosphere. In the above consideration of the question, the
emissive powers, a, /3, y...., are assumed to be independent of
temperature.
The discussion explains how it is to be expected that from the
temperature at the earth's surface we can hope to draw conclusions
about the temperature radiation of the whole atmosphere.
CHAPTER IV
A. INSTRUMENTS
For the following' observations I used one or more nocturnal com-
pensation instruments, pyrgeometers of the type described by K.
Angstrom in a paper in 1905.1 Without going into details, for which
I refer to the original paper, it may be of advantage to give here a
short description of the instrument.
Founded on the same principle of electric compensation used in
the Angstrom pyrheliometer, the instrument has the general form
indicated in figure 2. There are four thin manganine strips (M) , of
which two are blackened with platinum black, the other two gilded.
On the backs of the metal strips are fastened the two contact points of
a thermo junction, connected with a sensitive galvanometer G. If
the strips are shaded by a screen of uniform temperature, the thermo-
j unctions will have the same temperature, and we may read a certain
zero position on the galvanometer. If the screen is removed and
the strips are exposed to the sky, a radiation will take place, which
is stronger for the black strips than for the bright ones, and there
will be a deflection on the galvanometer due to the temperature
difference between the strips. In order to regain the zero position
of the galvanometer, we may restore the heat lost through radiation
by sending an electric current through the black strips. Theoretical
considerations, as well as experiments made, show that the radiation
is proportional to the square of the current used, that is,
R = ki2
where k is a constant that depends upon the dimensions, resistance,
and radiating power of the strips. As the radiating power from
the strips is difficult to compute, the constant k is determined from
experiment with a known radiation. The strips are exposed to
radiate to a black hemisphere of known temperature Tlt and the
constant is determined by the relation :
where T is the temperature of the strips. The advantage of this
construction over the form used for instance by Exner and Horaen,
where the effects of conduction and convection are also eliminated,
1 Nova Acta Reg. Soc, Sc. Upsal., Ser. 4, Vol. 1, No. 2.
28
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
29
lies in the possibility of measuring the radiation to the whole sky
and not only to a part of it, which is the case when one of the strips
must be shaded. It must always be regarded as a dangerous approxi-
^4
EL~
JTffTV ,.,M
= liiiiliiiiliiiiliinliiiilmiliii
7
F A B E
Fig. 2. — The Pyrgeometer.
mation to compute the radiation to the whole sky from the radiation
to a fraction of it, assuming a certain standard distribution of radia-
tion to the different zones of the sky. The method of adding up
30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
different portions is too inconvenient and fails when the radiation is
rapidly changing.
On the other hand, the value k is here dependent on the accuracy
with which the radiation constant a is determined. Further, since
the emissive power of the strips, which is different for different wave
lengths, enters into the constant k, this constant can be applied only
for cases where the radiation is approximately of the same wave
length as in the experiment from which k is computed. In the night-
time this may be considered the case, the emissive power being the
same for all heat waves longer than about 2 /*. But the instrument
cannot, without further adjustment, be used for determining the
radiation during the day, when the diffused radiation from the sky
of short wave length enters as an important factor.
The constants of my three instruments, of which No. 17 and No. 18
were used at Bassour and California, and No. 22 in California, have
been determined at the Physical Institute of Upsala on two occasions,
before the expeditions by Dr. Lindholm of that Institute and after
the expeditions by myself. The two determinations of the constants
differ from one another only within the limits of probable error.
No. Before After Mean
17 IO.4 IO.4 IO.4
18 I I.I IO.7 10.9
22 II.6 II.8 II. /
For the computations from the Algeria values the first values of the
constants (for 17 and 18) have been used, for the California observa-
tions a mean value between them both. For the determination of the
constants, Kurlbaum's value for o- has been used
(7 = 7.68- 10-11
not so much because this value is at present the most probable per-
haps, as in order that observations with these instruments may be
directly comparable with those of older ones. At any rate the rela-
tive values of the radiation must still be looked upon as the most
important question.
The galvanometers that I have used were of the d'Arsonval type.
They were perfectly aperiodic, and had a resistance of about 25 O and
a sensitiveness of about 2 • io-8 amp. per mm. at meter distance. They
generally showed a deflection of between 30 and 70 mm., when the
strips were exposed to a clear sky. The galvanometers and the
pyrgeometers were made by G. Rose, Upsala.
In the use of the compensation instrument one has to be careful
that the instrument has had time to take the temperature of the
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 3 1
surroundings before measurements are made. If the instrument is
brought from a room out into the open air, one can be perfectly safe
after ten minutes exposure. When measurements are made on the
tops of mountains or at other places where the wind is liable to be
strong, I have found it advantageous to place the galvanometer as
near the ground as possible. By reading in a reclining posture one
can very well employ the instrument box itself for the galvanometer
support. Some heavy stones placed upon, at the sides, and at the
back of the box will keep the whole arrangement as steady as in
a good laboratory, even when the wind is blowing hard.
For the measurements of the current used for compensation
milliammeters from Siemens and Halske were employed.
The measurements of the humidity, as well as of the temperature,
were carried out with aid of sling psychrometers made by Green
of Brooklyn. The thermometers were tested for zero, and agreed
perfectly with one another.
In order to compute the humidity from the readings of the wet
and dry thermometers I have used the tables given by Fowle in the
Fifth Revised Edition of the " Smithsonian Physical Tables " 1910.1
B. ERRORS
The systematic error to which the constants of all the electric
pyrgeometers are subject has already been discussed. There are
however some sources of accidental errors in the observations, and
I shall mention them briefly. The observer at the galvanometer will
sometimes find — especially if there are strong and sudden wind gusts
blowing upon the instrument — that the galvanometer does not keep
quite steady at zero, but swings out from the zero position, to which
it has been brought by compensation, and returns to it after some
seconds. The reason for this is probably that the two strips are
not quite at the temperature of the surroundings. From measure-
ments on the reflection of gold, it appears that the bright strip must
radiate about 3 per cent of the radiation of a black body, consequently
it will remain at a temperature slightly lower than that of the sur-
roundings, which will sometimes cause a slight disturbance *due to
convection, the convection being not perfectly equal for the two strips.
Another cause of the same effect is the fact that the strips are covered
1 These tables are calculated from the formula
p = pi — o.ooo665 (t — ti) (1 + 0.00115*1)
(Ferrel, Annual Report, U. S. Chief Signal Officer, 1886, App., 24).
32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
by a diaphragm to about i mm. from the edges. On this part of its
length the black strip will be heated but will not radiate, and the edges
will therefore be slightly above the temperature of the surroundings.
As I have made a detailed study of these edge-effects in the case of the
pyrheliometer,1 where I found that they affected the result only to
about 1 per cent, I will not dwell upon them here. In the case of the
pyrgeometer, the influence will result only in an unsteadiness of the
zero, due to convection currents. The two mentioned effects will
probably affect the result to not more than about ±2 per cent, even
under unfavorable conditions.
Much larger are the accidental errors in the measurements of
the humidity. The ventilated psychrometer, used in these measure-
ments, has been subjected to several investigations and critical dis-
cussions and it is therefore unnecessary to go into details. It will
be enough to state that the results are probably correct to within
5 per cent for temperatures above zero, and to within about 10 per
cent for temperatures below o°.
1 Met. Zeit, 8, 1914, p. 369.
CHAPTER V
I. OBSERVATIONS AT BASSOUR
The observations given in tables I and II were made at Bassour,
Algeria, during the period July io-September 10, 1912, at a height
of 1,160 m. above sea level. In regard to the general meteorological
and geographical conditions reference may be made to the introduc-
tory chapter. Every observation was taken under a perfectly cloud-
less sky, which in general appeared perfectly uniform. In regard to
the uniformity of the sky, I may refer to chapter VI, where some
observations are given that can be regarded as a test of the uni-
formity of the conditions.
Table I
Date
July 10. .
11 . .
12. .
18..
19..
20. .
22. .
23..
24..
25..
29..
30..
31..
Aug. 1 . .
2. .
3--
4--
5--
6..
10. .
11. .
I3--
14..
15..
20. .
21 . .
22.. .
23--
24.-
26..
27..
29..
30..
Sept. 3..
4--
5--
6..
Time
9:
Q:
9:
664.4
663.6
662.9
663.I
662.6
661.9
664.O
663.5
664.9
665.I
666.7
664.7
662.3
662.9
663.5
663.2
665.7
666.9
662.7
662.6
665.4
667.7
669.8
667.9
665.7
663.4
665.I
665.6
664.3
666.7
664.O
661.5
666.7
Temperature
19. 1
24.I
25-4
20. 1
23-3
21.5
17.2
20.0
19.5
18.8
18.0
21.0
22.6
23.8
20.3
24.2
21 .2
21.4
23.6
25.0
22.8
19.5
18.6
20.6
18.9
20.8
17.9
20.8
22.0
21.5
21.5
24.4
20.3
13.8
11. 1
20.8
20.0
15-7
At
1.8
6.3
6.4
0.6
5.6
5-7
-0.5
1.8
3,4
4-2
2.4
1-5
0.0
-1.4
1-7
4-6
2.7
0.5
3.2
4-4
4.2
2.1
2.4
-1.0
0
0
o
o
0
0
0
o
0
0
0
o
0
o
0
0
0
o
0
0
0
0
0
o
o
o
0
0
0
0
0
0
0
0
0
o
o
0
33
91
56
71
66
63
66
211
69
59
38
39
87
69
201
7i
73
75
62
73
78
58
71
47
79
45
201
73
92
75
217
88
90
57
38
69
205
220
177
34
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
In table I are given : The date, the time of clay, the barometric
pressure B, the temperature of the air, the humidity (in mm. Hg.)
p, and the effective radiation R. The temperature fall between the
time of observation in the evening and the time of sunrise is indi-
cated by At.
Table II
p
3.50-4.50
4.50-5.50
5.50-6.50
t
p
R
t
P
R
t
p
R
19. 1
22.6
23.8
20.8
21.5
20.0
3.86
4.14
4.40
3.84
3.80
3.99
O.191
O.169
0.201
0. 192
0.217
0.220
22.0
II . I
20.8
5.46
4.98
4-57
0.175
O.169
O.205
17.2
23.6
20.8
5.66
5.89
6.45
0.211
0.173
0.201
21.3
4.00
O.I98
18.0
5-00
O.183
20.5
6.00
0.195
P
6.50-7.50
7.50-8.50
8.50-9.50
*
P
R
t
P
R
t
p
R
25.4
6.60
0. 171
20.0
7.80
O.169
24.1
9.42
0.156
21.5
7.08
0.166
19.5
8.36
0.159
20. I
9
7,2
O.166
21 .0
7.14
0.187
18.8
8.25
O.138
23.3
8
54
O.163
21.2
6.60
0.175
20.3
7-54
O.171
18.0
9
16
0.139
17.9
7-44
0.173
21-5
8.48
O.188
24.2
8
96
O.173
20.3
7.10
0.157
24.4
8.36
O.190
19.5
8
86
O.171
15.7
6.80
0.177
20.6
8
61
0.179
20.4
6.98
0.173
20.7
8.13
O.169
21.4
8.98
O.164
P
9.50-10.50
1 1. 90-13. 24
t
P
R
t
P
R
-
21.4
25.0
22.8
13.8
9.88
9.98
10.20
10.40
O.162
O.178
0.IS8
O.I38
18.6
18.9
11.90
13.24
O.I47
0.145
20.8
10. 12
0.159
18.8 | 12.57
O.I46
[
From figures la and lb, where the radiation (crosses) and the
humidity (circles) are given as functions of time, it is already evi-
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 35
dent that there must be a very close relationship between the two
functions. In the figures the humidity values are plotted in the
opposite direction to the radiation values. Plotting in this way we
find that the maxima in the one curve correspond to the maxima in
the other and minima to minima, which shows that low humidity and
high effective radiation correspond and vice versa.
The observations of table I are now arranged in table II in such
a way that all the radiation values that correspond to a water-vapor
pressure falling between two given limits, are combined with one
another in a special column. The mean values of humidity and
radiation are calculated and plotted in a curve aa, figure 3, which
gives the probable relation between water-vapor pressure and radia-
tion. Tables I and II show that the temperature of the air, and con-
sequently also that of the radiating surface, were almost constant
for the different series and ought not, therefore, to have had any
influence upon the form of the curve.
The smooth curve of figure 3 gives the relation between effective
radiation and humidity. If we wish to know instead the relation
between what we have defined as the radiation of the atmosphere
and the humidity, we must subtract the value of the effective radia-
tion from that of the radiation of a black body at a temperature of
200. The curve indicates the fact, that an increase in the water con-
tent of the atmosphere increases its radiation and that this increase
will be slower with increasing vapor pressure. It has been pointed
out in the theoretical part that this is to be expected from the condi-
tions of the atmosphere and from the laws of radiation. The relation
between effective radiation and humidity can further be expressed
by an exponential formula of the form :
^ = 0.109 + 0.134 • e'°-10p
or
R = 0.109+0.134 • io^0-957-" •
For the radiation of the atmosphere we get
£0 = 0.453-0.1 34 •c"0-10'3
That the radiation of the atmosphere, as a function of the water-
vapor pressure, can be given in this simple form is naturally due
to the fact that several of the radiation terms given through the
general expression (3), chapter III, have already reached their limit-
ing values for relatively low values of the water- vapor density. These
terms, therefore, appear practically as constants and are in the
empirical expression included in the constant term.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 37
It is therefore evident that our formula can satisfy the conditions
only between the limits within which the observations are made,
and that in particular an extrapolation below 4 mm. water-vapor pres-
sure is not admissible without further investigations. These condi-
tions will be more closely considered in connection with the observa-
tions made on Mount Whitney, where the absolute humidity reached
very low values.
For the case where p approaches very high values, the formula
seems to indicate that the radiation approaches a value of about 0.11
cal., which may show that the water vapor, even in very thick layers,
is almost perfectly transparent for certain wave lengths. This is
probably only approximately true, and the apparent transparency
would probably vanish totally if we could produce vapor layers great
enough in density or thickness. In a subsequent chapter I shall dis-
cuss some observations that indicate that this is the case, and also that
the formula given above must prove inadmissible for very great
densities.
2. RESULTS OF THE CALIFORNIA EXPEDITION
The observations were taken simultaneously at different altitudes :
(a) At Claremont (125 m.) and on the top of Mount San Antonio
(3,000 m.) ; (b) at Indio in the Salton Sea Desert (o m.) and on
the top of Mount San Gorgonio (3,500 m.) ; and (c) at Lone Pine
(1,150 m.), at Lone Pine Canyon (2,500 m.) and on the summit of
Mount Whitney (4,420 m.) .
A. INFLUENCE OF TEMPERATURE UPON ATMOSPHERIC RADIATION
Among the observations taken by this expedition I will first dis-
cuss some observations at Indio and Lone Pine separately, because
they indicate in a very marked and evident way the effect upon the
radiation of a very important variable, the temperature. The Indio
observations of the effective radiation are given in table III and are
graphically plotted in figures 17 and 18, where the radiation and the
temperature during the night are plotted as functions of time. As
will be seen from the tables, the humidity varied very little during
these two nights.
As long as the temperature during the night is constant or almost
constant, which is the case in mountain regions and at places near
the sea, the effective radiation to the sky will not vary much, a fact
that has been pointed out by several observers: Pernter, Exner,
Homen, and others. But as soon as we have to deal with climatic
conditions favorable for large temperature variations, the effective
38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
radiation to the sky must be subject to considerable changes also.
Such conditions are generally characteristic of inland climates and
are very marked in desert regions, where the humidity is low and the
balancing influence of the neighborhood of the sea is absent. Indio
is situated in a desert region. In the middle of the day the tempera-
ture reached a maximum value of 430 C. on the 23d and 460 C. on
the 24th of July. In the evenings at about 8 o'clock the temperature
was down to 300 C, falling continuously to values of 21 ° and 190 C,
respectively, in the mornings at 4 130, when the observations ceased.
From the curves it is obvious that there is a close relation between
the radiation and the temperature. Every variation in the tempera-
ture conditions is accompanied by a similar change in the radiation.
In fact a decrease in the temperature of the surrounding air causes
a decrease in the effective radiation to the sky. This is even more
obvious from the observations taken at Lone Pine on August 5 and
August 10, when very irregular temperature variations took place
during the nights. The humidity conditions appeared almost con-
stant. From the curves (figs. 19 to 21) can be seen how a change in
the one function is almost invariably attended by a change in the other.
In regard to the radiating surfaces of the instrument, one is pretty
safe in assuming that the total radiation is proportional to the fourth
power of the temperature, an assumption that is based upon the con-
stancy of the reflective power of gold and of the absorption power of
platinum-black soot within the critical interval. The radiation of
these surfaces ought, therefore, to follow the Stefan-Boltzmann law
of radiation. For the radiation of the atmosphere we thus get :
Eat =Est — Rt
Knowing Est and Rt, of which the first quantity is given by the
radiation law of Stefan, to which I have here applied the constant
of Kurlbaum ((7=7.68 • io-11), and the second quantity is the effec-
tive radiation measured, I can calculate the radiation of the atmos-
phere. We are led to try whether this radiation can be given as a
function of temperature by an expression
Eat = C-T° (I)
similar in form to the Stefan-Boltzmann formula, and in which a
is an exponent to be determined from the observations. From ( 1 )
we obtain :
log Eat = log C + a log T
Now the observations of every night give us a series of correspond-
ing values of Eat and T. For the test of the formula (1) I have
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 39
chosen the observations at Indio during the nights of July 23 and
24, and at Lone Pine on August 5 and August 11. I have preferred
these nights to the others because of the constancy of the humidity
and the relatively great temperature difference between evening and
morning values. By means of the formula connecting radiation and
humidity obtained from the Algerian values at constant temperature,
a small correction may be applied to these Californian observations,
in order to reduce them to constant humidity. The logarithms of
the radiation values thus obtained are calculated and also the loga-
rithms of the corresponding temperatures, tables III and IV. If log
Eat is plotted along the ^-axis, log T along the Jtr~axis, it ought to be
possible to join the points thus obtained by a straight line, if the for-
dv
mula (2) is satisfied. The slope of this straight line ( -^=con-
dx
stant = a) ought in such a case to give us the value of a.
I have applied this procedure to the observations mentioned and
found that within the investigated interval the logarithms of radia-
tion and of temperature are connected to one another by a linear
relation. Figure 4 gives the logarithm lines corresponding to the
Indio observations. The deviations from the straight lines are some-
what larger for the Lone Pine values, but the discrepancies seem not
to be systematic in their direction and I therefore think that one may
regard the formula (1) as satisfied within the limits of the variation
that can be expected as a result of the many atmospheric disturb-
ances. The following table gives the values of a obtained from the
observations on the four nights selected:
Place Date
Indio July 23
Indio July 24
Lone Pine August 5
Lone Pine August 11
Weighted mean : a = 4.03.
The table shows that the value of a is subject to considerable varia-
tions, which is a natural consequence of the great variations from the
average conditions, to which the atmosphere is subject. In the fol-
lowing pages, when I have used the value 4.0 as an average value for
a, in order to reduce the various observations to a constant tempera-
ture (200 C), this procedure is held to be justified by the preceding
discussion, as well as by the fact that, in applying this method of
reduction, we obtain an almost constant value for the radiation
during the night, if we reduce it to a constant humidity. For
all other values of a, we shall get a systematic increase or de-
a
Weight
3.60
4
4.27
4
44
I
44
I
40
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table III — Radiation and Temperature
Jndio, July 23, 1913
273+ ' = 7"
LogT
Eat
Log Eat
302.5
301. 1
298.2
297.7
296.6
296.3
295.2
294.O
2 . 4807
2.4787
2.4745
2.4738
2.4722
2.4717
2.4701
2.4683
0.447
0.435
O.421
O.419
O.423
0.415
O.409
O.402
O.6503—I
O.6385—I
O.6243 — I
0.6222 — I
O.6263 — I
O.6180 — I
O.6117— I
O.6042 — I
Tndio, July 24, 1913
302.5
2.4807
* 0.461
0.6637—1
300.5
2.4778
0.446
0.6493—1
298.O
2.4742
0-435
0.6385-1
296.9
2.4726
0.424
0.6274 — 1
296.O
2.4713
0.418
0.6212- — 1
296.O
2.4713
0.418
0.6212 — 1
294.2
2.4686
0.405
0.6075—1
294.2
2.4686
0.405
0.6075—1
293.6
2.4678
0.405
0.6075—1
292.5
2.4661
0.407
0.6096 — 1
Table IV — Radiation and Temperature
Lone Pine, Aug. 5, 1913
273 + t = T
LogT
Eat
Log Eat
297.6
2.4736
0.391
O.5922—I
296.O
2.4713
0-374
O.5729—I
290. I
2 . 4624
0.336
O.5263—I
294.4
2 . 4689
0.374
O.5729—I
288.6
2.4603
0.336
O.5263—I
285.4
2.4555
0-333
O.5224—I
287.8
2-4591
0.335
O.5250—I
287.4
2.4585
0-343
0.5353—1
287.4
2.4585
0.351
0-5453—1
Lone Pine, 1
^.ug. II, 1913
293-5
2 . 4676
0.376
O.5752—I
297.6
2.4736
0.393
0-5944—1
296.2
2.4716
0.388
O.5888—I
293-7
2.4679
0.367
O.5647—I
291.9
2.4652
0-343
0.5353—1
287.3
2.4583
0.337
O.5276—I
285.0
2.4548
0.324
O.5105— I
284.8
2.4545
0.323
O.5092—I
282.8
2.4515
0.313
0.4955—1
283.0
2.4518
0.334
0-52.37—1
281.9
2.4501
0.319
O.5038—I
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
41
crease in the radiation with the time owing to the fact that the
temperature is always falling from evening to morning.
It is of interest to find that the value of a, thus determined, is in
close agreement with the value deduced by Bigelow * from thermo-
dynamic considerations of the heat processes to which the atmos-
Fig. 4. — Atmospheric radiation and temperature. Indio, Cal., 1913.
Log £a/ = Const, -f- a log T.
phere is subject. Bigelow finds a to be equal to 3.82 and almost
constant at various altitudes.
In regard to the connection that probably exists between the
effective temperature of the air and the temperature at the earth's
surface, I may refer to the theoretical treatment given in chapter III.
1 Boletin de la Oficina Meteorologica Argentina, Octubre, 1912, p. 15.
42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
B. OBSERVATIONS ON THE SUMMITS OF MOUNT WHITNEY (4,420 M.),
OF MOUNT SAN ANTONIO (3,000 M.), OF MOUNT SAN GORGONIO
(3,500 M.), AND AT LONE PINE CANYON (2,500 M.).
These observations will be discussed further on in connection with
the observations made simultaneously at lower altitudes. Here they
will be considered separately in regard to the conditions of tempera-
ture and humidity prevailing- at the high level stations. The problem
to be investigated is this : Is the effective radiation, or the radia-
tion of the atmosphere, at the high stations in any way different
from the radiation found at lower altitudes, under the same condi-
tions of temperature and humidity? Or is the average radiation of
the atmosphere, at the altitudes here considered, a constant function
of the temperature and the humidity? Will there not be other
variables introduced when we move from one place to another at
different altitudes? In the theoretical part I have pointed out some
facts that ought to be considered in this connection and I then arrived
at the conclusion that the effect on the radiation of temperature and
humidity ought to prevail over other influences in the lower layers
of the atmosphere.
The observations are given in tables 16 to 19. The tables also give
the radiation of the atmosphere corresponding to each individual
observation, as well as this radiation reduced to a temperature of
20° C. by means of the relation :
where a is assumed to have the same value as that obtained from our
observations at Indio and at Lone Pine. The observations given
in tables 16 to 19 are now arranged in tables V and VI in a way
exactly similar to that which I have employed for the Algerian obser-
vations, except that in tables V and VI, I deal with the radiation of
the atmosphere toward the instrument, instead of the reverse, as in
table II. The relation of the two functions has been explained above.-
From the tables it is seen that the Mount Whitney values, reduced
in the way described, seem to fall to values a little lower than what
would correspond to the form of the Algerian curve, as given above
by the formula Ea =0.453 — ai34 ' e~0'10p. The reason for this
discrepancy may be partly that the exponent a is not quite the same
for thin as for thick radiating layers. This explanation is rendered
unlikely by the calculations of Bigelow and the observations of Very
and Paschen on radiating layers of moist air. But there are other
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 43
Table V — Aft. Whitney and Alt. San Gorgonio
p
0.5-
-1.0
1.5-
-2.0
2.0-2.5
p
0.69I
0.69 J
Ea
p
*a
P
Ea
O.30O I
80
0.288
2.37
O.289
0.303 I
91
0.295
2.37
O.316
o.54l
0.54 J
0 . 298 I
54
O.289
2.46
0.338
O.297 I
88
O.274
2.46
0.337
68
O.260
2.06
0.317
Means
0 62
0 . 299 I
70
76
0.339
O.317
0.334
O.295
2.21
1.0-
-1.5 J
76
O.306
2.21
O.267
73
81
0.314
O.312
2.00
O.281
p
R I
2.00
O.262
81
0.302
2.32
O.326
1. 17
0 . 300 I
86
0.3l8
2.32
0.319
1.17
0.303 I
86
0.309
2.44
0.324
1.02
0.325 I
90
0.304
2.44
0.327
1.02
O.322 I
90
0.303
2.42
0.315
1 .12
O.316 I
83
O.308
2.42
0.315
1-47
0.3II I
83
0.303
2.46
O.308
i.47
0.393 I
93
O.298
2.46
0.314
1.47
0 . 260 I
93
O.285
2.39
0.315
1.32
0.323 I
52
0.335
2.39
0 . 309
1.32
0.316 I
52
0.332
2.21
O.299
1.40
0.316
1 .40
0.321
1. 14
0.276
Means
1.27
0 . 306 I
78
0.305
2.31
0.310
P
2.5-3-0
3-0-3.5
3.5-4.0
p
Ea
P
E
La
P
£a
2-95
2.66
2.61
2-97
2.90
2.59
2.59
2.74
2.74
2.87
2.87
2.67
2.67
O.300
O.282
O.288
0.335
0.344
O.311
O.308
0.313
O.302
O.326
O.317
0.332
0.317
3
3
3
3
3
3
3
3
3
07
35
35
28
28
18
15
30
23
0.351
0.337
0.345
0.310
0.304
O.329
0.350
O.271
O.327
3.80
3.80
3-75
3.6l
3-79
3.8l
3.70
3-59
3-59
3.51
3.51
O.277
0.338
O.306
0.343
0.345
0.320
0.302
0.344
0.330
0.356
o.35i
Means
2-75
0.313
0.325
3.68
0.328
44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
influences that are likely to produce a deviation of the same kind.
Among these we will consider :
( 1 ) The influence of the temperature gradient. It is evident
that for a radiating atmosphere of low density, a larger part of the
radiation reaching the surface of the earth must come from farther
and therefore colder layers than for a dense atmosphere. From this
it follows that a decrease in the density of the atmosphere must
produce a decrease in its radiation in a twofold way: (A) in con-
sequence of the diminished radiating power of the unit volume; and,
(B) because of the simultaneous shifting of the effective radiating
layer to higher altitudes.
(2) We must consider that the radiation is determined by the
integral humidity, and that the water-vapor pressure comes into play
only in so far as it gives a measure of this quantity. At a certain
place we may obtain the integral humidity by multiplying the pressure
by a certain constant ; but this constant varies with the altitude. At
sea level this constant has a value equal to 2.3 against 1.8 at the alti-
tude of the summit of Mount Whitney ; these values can be obtained
from the formula of Suring, which has been discussed in a previous
chapter.
This means that, in order to compare the integral humidities of
two different localities as indicated by their absolute humidities, we
should apply a reduction factor to the latter values. Thus, if the
absolute humidity on the top of Mount Whitney is the same as at
sea level (which naturally is unlikely to be the case at the same time),
1 8
the integral humidity at the former place will be only -1- of that at
the latter.
(3) The coefficient of absorption, and consequently also that of
the emission for a unit mass of water vapor, is a function of the total
pressure to which it is subjected. This important fact has been
revealed by the investigations of Eva von Bahr * who found that water
vapor at a pressure of 450 mm. absorbs only about 77 per cent of
what an identical quantity absorbs at 755 mm. pressure. The ab-
sorption coefficient will change in about the same proportion, and
consequently the effective amount of water vapor .(if we may use
that term for the amount of water vapor that gives a constant radia-
tion) will not be proportional to its mass but will be a function of
the pressure, i. e., a function also of the altitude. Miss v. Bahr's
1 Eva v. Bahr, Tiber die Einwirkung des Druckes auf die Absorption
Ultraroter Strahlung durch Gase. Inaug. Diss., Upsala, 1908, p. 65.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
45
measurements unfortunately do not proceed farther than to the
water-vapor band at 2.7 /x and include therefore a part of the spectrum
that is comparatively unimportant for the " cold radiation " with
which we are dealing here. The maximum of radiation from a black
body at 285 degrees absolute temperature occurs at about 10 n, and
Table VI — Mt. San Antonio and Lone Pine Canyon
p
1 . 50-2 . 50
2.50-3-50
3.50-4.50
p
Ea
P
Ea
P
Ea
2.27
2.16
1.63
2.27
1.99
2.36
2.22
2.46
O.310
O.310
O.309
0.313
0.324
0.312
O.321
0.335
2.54
2.65
3.24
2.60
3-23
O.363
0.334
0.340
O.346
0.357
3.63
3.63
3-91
3-9i
3-53
4.23
4-07
3-75
4.00
0.348
0.355
0.357
0.350
O.361
0.334
0.345
0.334
0.333
Means
2. 17
0.317
2.85
0.348
3.85
0.346
Means.
4.50-5.50
5.09
0.359
0.346
0.351
o . 382
0.375
0-397
0.368
5-50-
-6.50
p
Ea
6.48
0.358
6.35
O.362
6.35
0.352
6.06
0.371
5-93
O.378
5.88
0.374
5.52
0.375
6.09
5.98
O.39I
0.38.3
5.98
O.386
6.30
O.372
6.08
0.373
6.50-7.50
p
Ea
7.34
6.53
0.359
O.367
6.94
O.363
7.50-8.50
P 1 Ea
7.85
7.85
7.63
0.356
O.366
0.376
7.78
0.366
therefore we cannot apply the numerical results of Miss v. Bahr to the
radiation of the atmosphere.
At any rate, the conclusion seems to be justified that if we take
the absolute humidity at the place of observation as a measure for
the radiating power of the integral water vapor, the result would be
46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65'
liable to give too high values at the higher altitude as compared with
the lower one. This is actually the result of the observations. It
therefore appears to me that the observations lend support to the
view that the variations produced in the radiation of the lower atmos-
phere by a change of locality or by other influences are due to
changes in the radiating power of the water vapor; changes that
we are able to define, within certain limits, from observations of
the temperature and the humidity at the surface of the earth.
I have now, without venturing to emphasize the absolute reliability
of the procedure, applied a correction to the observed vapor pres-
sure at different altitudes, in order that the pressure may give a
true measure of the integral radiating power of the water vapor.
Considering that at the altitude of Mount Whitney, the constant K
in Suring's formula is 1.8, and that the total pressure there is only
44 cm., so that the absorption coefficient according to Miss v. Bahr's
observations should be — — of the value corresponding to p — 66 cm.
(Lone Pine, Bassour), and finally that the pressure ought to be
reduced to the temperature 200 C, I have used the reduction factor
l8 16,5 m =0.68
2.2 21.5 293
for the humidity values taken at the summit of Mount Whitney
(4,420 m.) and also for Mount San Gorgonio (3,500 m).
A similar consideration gives the reduction factor
2X, _ 19,5.288 =og
2.2 21.5 273
for the measurements at Mount San Antonio (3,000 m.) and at
Lone Pine Canyon (2,500 m.).
In this way the values plotted in figure 5 are obtained. We are
now able to draw a continuous curve through the points given by
the observations corresponding to various altitudes. With regard
to the considerations that I have brought forward in the theoretical
part, I have tried an expression of the form
Ea=K-Ce~yp
where
K = 0.439, C = 0.158, and 7 = 0.069.
This gives a fairly good idea of the relation between the radiation of
the atmosphere at 200 C. and the humidity. The curve corresponding
to this equation is given by a dotted line in figure 5. The expression
adopted here does not fit the observations at high pressures so
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
47
well as the expression given in connection with the discussion of
the values obtained at Bassour, but it is better adapted to include in
a general relation all the observations at different altitudes. As may
be seen from the figure, the deviation from the curve is often consid-
erable for single groups of values, but this can easily be explained
as being due to deviations of the state of the atmosphere from its
.45
.45
X
3——
i — %
X
<
^
■■ ■'"
©^>-
■X.
■>
X
x ^
.35
/
.35
@
y
* ®
/ •
,
/
K
.30
•J
/ •
.30
^
'
/
/
'
.25
.25
i
1
Fig. 5. — Humidity and Radiation of the Atmosphere. p
Circles represent observations at Indio. Double circles represent observa-
tions at Mount San Antonio and at Lone Pine Canyon. Crosses represent
observations at Lone Pine. Points represent observations at Mount San
Gorgonio and at Mount Whitney.
normal conditions and also to the fact that the mean value is often
calculated from a few observations.
It seems to me that the form of this curve enables us to draw some
interesting conclusions about the radiation from the different con-
stituents of the atmosphere. It must be admitted that the shape of
the curve in the investigated interval does not allow of drawing any
safe conclusions for points outside this interval, and particularly,
as will be shown further on, the curve does not approach a limiting
48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
value of 0.439 caL f°r very lartee values of p, as one would expect
from the expression that has been adopted. On the other hand, the
observations bring us very near the zero value of humidity and the
question arises, whether we may not be entitled to attempt an extra-
polation down to zero without causing" too large an error in the limit-
ing value. We wish to answer the question : how does the atmosphere
radiate, if there is no water vapor in it? As I have pointed out
previously, the possibility of an extrapolation to zero is doubtful,
because in the non-homogeneous radiation of the water vapor there
are certainly terms corresponding to wave lengths, where even very
thin layers radiate almost to their full value. Consequently these
have scarcely any influence upon the variations of the radiation from
thicker layers. Will the curve that gives the relation between the
radiation and the radiating mass of water vapor for values of the
humidity lower than 0.4 show a rapid decline of which no indication
is apparent in the investigated interval 0.4—12 mm.? For compari-
son I may refer to a curve drawn from a calculation by N. Ekholm *
of the transmission of water vapor according to Langley and
Rubens and Aschkinass. The curve represents the radiation from
a black body at 150 temperature as transmitted through layers of
water vapor of variable thickness. The same curve evidently also
gives the radiation from the identical vapor layers, provided that
the law of Kirchhoff holds, and that the water vapor itself is at 15 °.
As far as the result may be depended upon, it apparently shows
that laboratory measurements give no evidence whatever of a sudden
drop in the radiation curve for very thin radiating layers. It would
be rather interesting to investigate the radiation of the atmosphere
compared with the radiation of the water vapor and of the carbon
dioxide and possibly also that of the ozone contained in the upper
layers, with proper regard to the temperature conditions and to care-
ful laboratory measurements on the absorption and radiation of these
gases. A first attempt in this direction is made by Ekholm. How-
ever, it appears to me that he does not give due attention to the fact
that the magnitude of the effective radiation to space depends upon
the capacity of the atmosphere to radiate back to the earth, and
only indirectly upon the absorption capacity of the atmosphere.
Quantitative calculations of the radiation processes within the atmos-
phere must necessarily take into consideration the temperature con-
ditions in various atmospheric layers. The laboratory measurements
upon which such a computation should be based are as yet very in-
Met. Zt., 1902, pp. 489-505.
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 49
complete and rather qualitative than quantitative, at least as regards
water vapor. I have reason to believe that the careful observations
of Fowle, of the Astrophysical Observatory of the Smithsonian
Institution, will in the near future fill this gap.
From analogy with the absorbing qualities of water vapor, I think
one may conclude that an extrapolation of the radiation curve (fig. 5)
down to zero is liable to give an approximately correct result. The
extrapolation for the radiation of a perfectly dry atmosphere at 20° C.
gives a value of 0.281, which corresponds to a nocturnal radiation
of 0.283 at the same temperature. At o° C. the same quantities are
0.212 and 0.213 cal. and at —8° they have the values 0.190 and 0.191,
respectively. The latter value comes near the figure 0.201, obtained
by Pernter on the top of Sonnblick at —8° C. temperature.
These considerations have given a value of the radiation from a
perfectly dry atmosphere, and at the same time they lead to an ap-
proximate estimate of the radiation of the upper atmosphere, which
is probably chiefly due to carbon dioxide and a variable amount of
ozone. The observations indicate a relatively high value for the
radiation of the upper layersi — almost 50 per cent of the radiation
of a black body at the prevailing temperature of the place of observa-
tion. Hence the importance of the upper atmosphere for the heat-
economy of the earth is obvious. The effect at places near the earth's
surface is of an indirect character, as only a small fraction of the
radiation from the upper strata reaches the earth's surface. But the
importance of the upper layers for the protecting of the lower water-
vapor atmosphere — the troposphere — against loss of heat, is entirely
similar to the importance of the latter for the surface conditions of
the earth. If we could suddenly make the upper atmosphere dis-
appear, the effect would scarcely be appreciable at the earth's surface
for the first moment. But the change would very soon make itself
felt through a considerable increase in the temperature gradient.
At places situated a few kilometers above the earth's surface, as, for
instance, the summits of high mountains, the temperature would fall
to very low values. As a consequence the conduction and convection
of heat from the earth's surface would be considerably increased.
Keeping these conditions in view, and in consideration of the high
value of the radiation of the upper atmosphere — -the stratosphere —
indicated by the observations, I think it very probable that relatively
small changes in the amount of carbon dioxide or ozone in the atmos-
phere, may have considerable effect on the temperature conditions
of the earth. This hypothesis was first advanced by Arrhenius, that
50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the glacial period may have been produced by a temporary decrease
in the amount of carbon dioxide in the air. Even if this hypothesis
was at first founded upon assumptions for the absorption of carbon
dioxide which are not strictly correct, it is still an open question
whether an examination of the " protecting- " influence of the higher
atmospheric layers upon lower ones may not show that a decrease
of the carbon dioxide will have important consequences, owing to the
resulting decrease in the radiation of the upper layers and the in-
creased temperature gradient at the earth's surface. The problem
is identical with that of finding the position of the effective layer in
regard to the earth's radiation out to space. I propose to investigate
this subject in a later paper, with the support of the laboratory
measurements which will then be available.
C. OBSERVATIONS AT INDIO AND LONE PINE
Knowing the influence of temperature upon the radiation of the
atmosphere, I can reduce the radiation values obtained at different
places to a certain temperature. The function giving the relation
between radiation and water-vapor content ought to be the same
for every locality. Reducing the observations at Bassour, at Lone
Pine, and at Indio (see tables VII and VIII) to 200 C, and plotting
the mean values, we obtain a diagram of the aspect shown in figure
5. The values from Algeria are given by. the smooth curve. The
observations from Lone Pine (crosses) and the observations from
Indio (circles) deviate more or less from the Algerian curve. Con-
sidering, however, that they are founded upon a very limited number
of nights (Lone Pine 8, Indio 3), and that the mean deviation for
all points is very inconsiderable, the result must be regarded as very
satisfactory.
In regard to the general meteorological conditions at Lone Pine,
it must be said that this place proved to be far from ideal for this
kind of observation, the principal purpose here being, not to collect
meteorological data, but to test a general law. The rapid changes
in temperature and humidity during the nights must have had as a
result that the atmosphere was often under very unstable conditions,
widely differing from what may be regarded as the average. This
is obvious also from the balloon observations of the U. S. Weather
Bureau, made simultaneously with my observations during a couple
of evenings at Lone Pine. These observations, made up to about
2,000 meters above the place of ascent, showed that there were often
considerable deviations from the conditions defined by " the con-
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
51
?
in On t)-
TT TJ" CO
t^ On coo O co 10
O h N « N n h
T Tj- TJ- Tf- -sf Tt" ^T
0 0 0 0 o* o o
O O O O O On O
c?\ r^ w i-H r^NO 00 ^f^i-r^oooMD ioci 00 o -* on co o toNNio
0OMN- O O O Oi O00 NO KNaO t^oo 00 00 00 On O On co ^O
o 0 0 0 o 0 o 0 o d o 0 0 o o 0 o" 0 0 0 0 o 0 d d d
00 00 t^oo 00 00 00 r^oo r^ r^ r^oo 00 00 00 i^oo 0000000000 t^r^t^
no MnuiaOON OOO <N 00 urtTf O00 coo OnOn
m on 000 o 10 no i^no vn« mno\ t^o o r^ r-^ 100
COCOCOCOCOCOCOCOCOCOincOcOCOCOCOCOCOCOCOCO
o d d d 0" d d d o d d d d 00060000
nono nnnnnk r^o nooo r^t^c^r^t^r^r^w
NO00 OO 0>Kh\o 1-1 1-1 COCO ON m in co •* N r^ On r-^
\o 10 100 t-^ r-^00 lo t>. r^N.o m^N iono ^too 00 00 o
cocococococococococococococococococococococo
d d d d d d 0000 d d d d o o d d d d d d
t^ On co I^O O Ol CN10000000000000000 t — 1 — >— 1 mono
oor^cooNONTj-M h kkkkh m knn <m aoMmo
10 100 10 100 no o in in in ino no in ino o in in in in
mh m ow cool o Onoo in tj- in ono in
\D CO O no r^O moo 00 coNO nooo ^-ioo
cococococococococococococococOTt-
o o" d d d d 6666066660
OhhwOOOOOOnoOOn t^O no O O <N
TrNNtoroOOCINNOrOHHtotONt
inxfM"inininininm'rt-inininininin
tj- c\) r^No 00 n
t^oo i^» ^o in
COCOCOCOCOCO '
6 6 6 6 6 6
NNullOOvO
OO00 00 Tf Tf
co co co co -rt Tj-
52
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
stant temperature gradient " and by Suring's formula for the water-
vapor pressure.
But the purpose of observations of the kind here described is a
double one. In the first place, to find the general law for the average
conditions, and in the second place to give an idea of the deviations
likely to occur from these average conditions.
Table VIII — Indio
9
8 . 0-9 . 0
9.0-10.0
p
£a
P
£a
8.15
8.43
8.81
O.4OO
0.393
0-393
9.65
9-37
9-30
9.65
0.397
0.398
0.399
0.404
Means
8.46
0.395
9-49
0.400
IO.O-II.O
10.31
10.69
10.97
10.82
10.52
10.52
10.47
10.67
10.77
10.64
Means \ 10.64
0.402
0.405
0.410
0.396
0-395
0.397
0.402
0-435
0.440
0.436
0.412
11. 0-12.0
II
86
II
43
II
13
II
33
II
30
II
56
II
4i
H-43
0.436
0-433
0.438
0.396
0.391
0-394
0.396
0.412
D. THE EFFECTIVE RADIATION TO THE SKY AS A FUNCTION OF TIME
Exner1 has made a comparison between the radiation values ob-
tained at different hours of the night on the top of Sonnblick. He
finds that there are indications of a maximum of radiation in the
morning before sunrise.
1 Met. Zeitschrift (1903), 9, p. 409.
1
-*
T
\-
cc
i 1
CO
\
A
/
/
CM
/
i
1
1
I
"-
I
/
/
i
/
/
/
/
i
CM
*
1
/
/
/
7
/
,/
1
o
/
/
/
/
/
/.
K1
/
.00 i
1 /
r
/
/
or
©—
V
/
o_
b
7
: co | cm t- o
Cal.
.20
.15
54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
From the observations on the nights of August 3, 4, 5, and 11 on
the summit of Mount Whitney (during these nights the observa-
tions were carried on continuously from evening to morning), I
have computed the means of the radiation, the temperature, and the
humidity, corresponding to different hours. The result is given by
figure 6, where the curve RR corresponds to the radiation; the
curves HH and TT to the humidity and the temperature, respectively.
The radiation decreases slowly from 9 o'clock in the evening to about
2 o'clock in the morning. At about 2:30 the radiation is subjected
to a rapid increase ; between 3 and 4 o'clock it keeps a somewhat
higher value than during the rest of the night. The temperature,
which shows a very continuous decrease from evening to morning,
evidently cannot be regarded as a cause for these conditions. An
examination of the humidity conditions shows however that the abso-
lute humidity is subjected to a very marked decrease, which is per-
fectly simultaneous with the named increase in the effective radiation.
Considering that the previous investigations, discussed in this paper,
show that low humidity and high radiation correspond to one another,
Ave must conclude that the maximum of radiation occurring in the
morning before sunrise, is caused by a rapid decrease of the humidity
at that time. It seems very probable to me that the maximum obtained
by Exner from his observations on Sonnblick, may be explained in
the same way.
E. INFLUENCE OF CLOUDS
The influence of clouds upon the radiation processes within the
atmosphere is of very great importance for many meteorological
questions. At the same time the problem is an immensely difficult
one, because of the irregularities of the fundamental phenomenon
itself. Take the question of the influence of the conditions of the
atmosphere upon the amount of radiation reaching us from the sun.
When the sky is clear, we can probably calculate from a single obser-
vation, or a couple of observations, together with one or two known
facts, the whole access of radiation during the day to within perhaps
5 per cent. But as soon as clouds are present, we have to fall back
upon continuous observations, the occurrence and density of the
clouds, and the time of their appearance being subject to no known
general law that holds for such small intervals of time as we wish to
consider. Moreover the influence of clouds upon the solar radiation
is very great, the radiation being reduced to a very small fraction of
its former value by the interference of a cloud. Similar condi-
tions hold in regard to the effective radiation to the sky. As this
u
u
u
u
^fe
Radiation,
cm.- mm.
56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
radiation goes out in all directions, the influence of a single cloud
will be more continuous than is the case for the solar radiation. As
soon as the cloud comes over the horizon it will begin to affect the
radiation to the sky, its influence growing as it approaches the zenith.
This will be rendered clearer, and details will be afforded, by the
observations on the radiation to different parts of the sky, given in
a later chapter.
It is evident that, when the sky is cloudy, we can distinguish be-
tween three radiation sources for the atmospheric radiation : First,
the radiation from the parts of the atmosphere below the clouds ;
secondly, the part of the radiation from the clouds themselves, which
is able to pass through the inferior layer, and, in the third place, the
radiation from the layers above the clouds, of which probably, for
an entirely overcast sky, only a very small fraction is able to penetrate
the cloud-sheet and the lower atmosphere.
Some measurements were taken in the case of an entirely overcast
sky. Figure 7 shows two curves drawn from observations at Clare-
mont. In the beginning the sky was perfectly clear, at the end it was
entirely covered by a low, dense cloud-sheet : cumulus or straro-
cumulus.
In general the following classification seems to be supported by the
observations :
Average radiation
Clear sky 0.14-0.20
Sky entirely overcast by :
Cirrus, cirrostratus and stratus 0.08-0.16
Alto-cumulus and alto-stratus 0.04-0.08
Cumulus and strato-cumulus 0.01-0.04
Especially in the northern winter climate, the sky is very often over-
cast by more or less dense sheets of stratus clouds. They are very
often not dense enough to prevent the brighter stars being very easily
seen through them, and especially in the night it is therefore often
difficult to tell whether the sky is perfectly clear or not. Dr. Kennard
proposed to me that one should use the visibility of the stars (1st, 2d,
3d, and 4th magnitude, etc.) to define the sky, when it seemed to be
overcast or very hazy. This may be of advantage, especially when
observations are taken in the winter time or extended to hazy condi-
tions.
CHAPTER VI
RADIATION TO DIFFERENT PARTS OF THE SKY *
In the foregoing chapters an account has been given of observa-
tions showing the influence of humidity and temperature conditions
upon the effective radiation to the sky. There the total radiation to
the sky was considered, independent of the fact that this radiation
takes place in different directions. The thing measured represented
an integral over the whole hemispherical space. About the different
terms constituting the sum this integral gives us no idea.
In the historical survey I have referred to the interesting investi-
gations of Homen, and mentioned his observations of the nocturnal
radiation to different parts of the sky. Homen observed, with a
somewhat modified Angstrom pyrheliometer, of type 1905, where
two metal disks were exposed to the sky alternately and their tem-
perature difference at certain moments read off. In order to measure
the radiation in various directions Homen used a screen arrangement,
which screened off certain concentric zones of the sky. The chief
objection to this method seems to me to be that the radiating power
of the soot will be introduced as a variable with the direction, and as
this quantity is not very well defined an error will probably be intro-
duced, which, however, can scarcely amount to more than about
2 per cent. Homen found that the distribution of the radiation upon
the different zones of the sky was almost constant for different values
of the total radiation. As Homen's measurements have since been
employed in extending, to represent the whole sky,2 observations of
the radiation toward a limited part of the sky, and as the question
itself seems to be of interest for the knowledge of atmospheric radia-
tion in its dependence upon other conditions, I have thought it valu-
able to investigate in what degree this distribution of radiation over
the sky is subject to variations. For this purpose the arrangement
shown schematically in figure 8 was found to be a satisfactory one.
To the electrical compensation instrument, which has been de-
scribed, can be attached a hemispherical screen, abcdef, whose radius
is 7.1 cm. From this screen can be removed a spherical cap cd, which
1 Large parts of this chapter were published in the Astrophysical Journal,
Vol. 39, No. 1, January, 1914.
2 Exner (1903), loc. cit.
57
58
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
leaves a hole of 320 plane angle open to the sky. The screen is brightly
polished on the outside, but blackened on the inside, in order to avoid
multiple reflections.
The instrument to which this arrangement was attached was
pointed to different parts of the sky, and the zenith angle was read
in a circular scale, as is shown in figure 8. The value of the radiation
within the solid angle csd (320) was obtained in the usual way
_<*
Fig. 8. — Apparatus used for determining the radiation to
different parts of the sky.
by determining the compensation current through the black strip.
This arrangement has two obvious advantages over a bolometer
arranged in a similar way. In the first place, the instrument is very
steady and quite independent of air current, because both strips are
here exposed in exactly the same way. The readings must further be
quite independent of the position of the strips, it being possible to
turn the instrument over in different directions without change in
the sensitiveness. Everyone who is familiar with bolometric work
knows the difficulty that sometimes arises from the fact that the
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 59
sensitiveness of the bolometer changes with its position, the con-
ductivity of heat from the strips through the air being different for
vertical and horizontal positions. On the other hand, the sensitive-
ness of my apparatus, used in this way, was not very great. When
the instrument was directed to points near the horizon the deflection
of the galvanometer seldom amounted to more than about 2 mm.,
and for zenith position the deflection was about 6 mm. The prob-
able error in every measurement is therefore about 5 per cent. In
spite of this disadvantage, a comparison between the values of the
total radiation observed and the total radiation computed from the
observations of the radiation to the different zones shows a fairly
close agreement.
If the dimensions of the strips can be regarded as negligible in
comparison with the radius of the screen, we may assume the effec-
tive solid angle to be equal to the solid angle under which the central
point of the instrument radiates to the hole. Now this is not exactly
the case, and in computing the total radiation from the radiation to
the limited parts of the sky, we must apply a correction with regard
to the position of the strips. The mean solid angle is obtained
through an easily effected but somewhat lengthy integration process
given in the foot-note.1 It is found to be 768.60.
The correction term will make 1.5 per cent in the solid angle, a
quantity that is not negligible when we wish to calculate the total
radiation.
When the instrument is pointed in different directions, different
parts of the strips will radiate to slightly different regions of the
sky. In the process used for finding the distribution of radiation
1 Let us consider a circular hole of the radius p, radiating to a plane surface,
parallel with the hole and at the vertical distance R from it. We wish to find
the radiation T to a little elementary surface, dx, whose distance from the
perpendicular from the central point of the hole, is /. Using cylindric coordi-
nates, and defining the element of the hole (do), through the relation:
0=piC
R2Pid<pdp
we get: dl =77^ .
[R2+Pi +/2— 2p±l cos <p] 2
and for the radiation from the entire hole:
27r axdad(p
' T-
where we have put :
[l+ai+/32— 2tt1|8 COS <p}2
R' ai—R-' P—R
6o
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
from the single measurements this would introduce a complication
if the instrument were not always turned over so that the strips
were parallel to the earth's surface. When this precaution is ob-
served, we may regard the influence of the dimensions of the strips
as negligible.
If a and (3 are not large, so that higher powers than the fourth may be
neglected, the integration gives :
7=7ra2(l— a2— 2^) dr (i)
Fig. 9.
Now we proceed to consider the case, where the hole radiates to a strip
of negligible width ds and of the length 2 m. The line is symmetrical in
regard to the perpendicular from the central point of the hole. For the
central point of the line we put : I = n. Then we have :
dr=zdm'ds
P R2 R2
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
61
The results of these measurements for various conditions are
given in table IX. Four series, representing different conditions
1
i
i
I
1
1
/
yr
1
i
1
/
/
i
!
!
!
\
/
/
A
i
i
i
/
i
(
i
!
i
1
/
1
\
1
/
i
i
1
1
1
/
I
i
i
i
1
/
i
i
1/
1
i
i
/
i
i
i
/
1
'
1
1
i
i
/
1
i
i
/
i
i
1
i
.
i
.,
i
90 80 70 60 50 40 30 20 10 o
Fig. 10.
in regard to the prevailing humidity, were taken at Bassour, Algeria,
at a height of 1,160 m. above sea level. Two series were taken on
Introducing this in (1) and integrating between the limits 0 and m, we
obtain for the radiation to the whole strip :
T'=irma2
L
, 2J_«M
2(W+TJ
R2
ds
(2)
My instrument contained two radiating strips : For the one was : m = 9.0 ;
n = 2.0. For the other one : m = 9.0 and n = 6.0. Further I had : R = 68.3 ;
P = 19.6.
As my unit of radiation, I will now define the radiation from a surface
equal to the surface of the strips within a solid angle whose cross-section
is a square, and each side of which subtends one degree. Introducing the
given values of a, m, n and R in (2), I then find that the mean radiation from
the two strips is 768.6 times my unit of radiation.
62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
top of Mount Whitney, 4,420 m. above sea level. In every instance
the sky was perfectly clear and appeared perfectly uniform. It will
be shown later on, that there is also strong experimental evidence
for the perfect uniformity of the sky.
In order to obtain from the observations a more detailed idea
of the effective radiation to different parts of the sky, I proceeded
in the following way : In a system of coordinates, where the
zenith angle is plotted along the jr-axis, the magnitude of the
radiation along the y-axis, every measurement with the instrument
corresponds to an integral extending over 32 ° and limited by the
.r-axis and a certain curve — the distribution curve of radiation. If
the measurements are plotted as rectangular surfaces, whose widths
are 320 and whose heights are proportional to the magnitude of the
radiation, we obtain from the observations a system of rectangles like
those in figure 10. A curve drawn so that the integrals between the
limits corresponding to the sides of the rectangles are equal to the
areas of these rectangles will evidently be a curve representing the
radiation as a function of the zenith angle.
(Note. — Against this procedure it can be objected that the observations do
not really correspond to rectangular surfaces, the opening being circular and
not square. The consequence will be that the real distribution curve will cut
the rectangles in points lying nearer their central line than the section points
defined by the procedure described. In fact this will alter the form of the
curves very slightly; in drawing them the conditions just mentioned have
been taken into consideration.)
In figures ha and iib the curves are shown. They indicate the
fact — which has already been pointed out by Homen — that the effec-
tive radiation to a constant area of the sky decreases with an increase
in the zenith distance. My observations indicate very strongly that
the radiation approaches the zero value, when the zenith angle ap-
proaches 900, which shows that the lower atmosphere, taken in very
thick layers, radiates like a black body. If there were no radiating
atmosphere at all, the distribution curve would be a straight line
parallel to the jr-axis.
A comparison between the different curves shows, further, that
they differ in a very marked way from one another in regard to their
form. It is also evident that th.s difference in form is very closely
connected with the density conditions of the atmosphere and espe-
cially with its content of water vapor.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
63
X
CO
OO
10
IX
w
&
0
O
0
O
0
tti
0
O
0
O
0
00
5
0
O'
0"
O
0
M
+
+
+
+
1
+
T3
OJ
ix
NO
r^
NO
0
3
On
r^
ON
t^
m
0.
E
0
I-1
1-1
l-l
w
i-1
6
■ 0
O'
6
0'
u
T3
a
"*■
00
<M
On
ix
10
M
ON
0
On
NO
m
Tf
rt
1-1
1-1
1-1
M
h- 1
m
rt
d
d
0'
6
O'
0
H
tX
M
<N
O
O
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NO
<N
6
O
CM
00
NO
Tt-
lO
0
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"3"
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hH O
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6
6
6
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0 0
6 6
6 6
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NO
■*
CO
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tx
NO
6
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Tt
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CN|
lO
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"tf"
M t^
t 00
lO Tf
CO CO
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d
6
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0 0
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0 0
r^
m
10
rf
0 •
0
r^
t^
t^
0'
6
NO
>-o
■*
lO
"«t
oo 10
t^ (M
O
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10 in
■<t -*
6
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XT Tf
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r-s
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in
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CO
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QJ
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OO
So
!ON
So
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(VI
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01
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Oq
i— 1
ON
ON
M
M
64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Together with the observations treated in the foregoing- chapters,
the present result gives us support for the following conclusions :
1. An increase in the water- vapor pressure will cause a decrease
in the effective radiation to every point of the sky.
2. The fractional decrease is much larger for large zenith angles
than for small ones.
If we regard the atmosphere as a plane parallel layer, having
uniform density, p, and a temperature uniformly equal to the tem-
perature at the earth's surface, the effective radiation of a certain
wave length, A, in different directions, may be expressed by
_7. p
Jx.= Ce cos* (1)
where C and y are constants and <j> is the zenith angle. For another
density, p, of the radiating atmosphere we have :
-7 p'
J\=Ce cos<p (2)
and from (i) and (2)
_lA — 0 r L cos d> J
LCOS0-I (3)
If p is greater than p, J\ will always be less than J\. It is evi-
dent from the relation (3) that the ratio between Jx and J\ dimin-
ishes as the zenith angle approaches 900. The general behavior of
the radiating atmosphere is therefore consistent with the case that
only a single wave length is radiated and absorbed. But the detailed
conditions are naturally very complicated through the lack of
homogeneity of the radiation. Especially for the curves correspond-
ing to high humidity the radiation falls off much quicker with the
approach to the horizon than is to be expected from the dependence
of the total radiation on the humidity. Especially is this the case
after we have reached a value of the zenith angle of about 60 or 70
degrees. In part this is due to the increasing influence of the radia-
tion of wave lengths whose radiation coefficients are small and can
be neglected for smaller air masses, but which for the very large air
masses that correspond to zenith angles not far from 900 must come
into play and produce a rapid decrease of the effective radiation
to points near the horizon. But here other influences are also to be
considered. The observations of the total radiation, compared in
regard to the diffusing power of the atmosphere for visible rays,
show that the influence of diffusion can be neglected in comparison
with the other more fundamental influences, as far as the total radia-
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
65
tion is concerned. But in regard to the radiation to points near the
horizon we must consider that the corresponding air masses become
very large and that effects of dust and haze and other sources of
lack of homogeneity in the air must be introduced in quite a marked
way.
jf 15
10
y\\
5
Ml
\\
N
Zenith distance.
Fig. i i a. — Radiation to different parts of the sky. Bassour observations.
The curves in figures iia and iib represent the effective radiation
within the unit of the solid angle in different directions from a sur-
face perpendicular to the radiated beam. From these curves we can
compute the radiation from a horizontal surface, like the earth's
surface, to the different zones of the sky. If the radiation within a
solid angle one degree square is R, the radiation (/) to the whole
zone, whose width is one degree, is expressed by :
J = R cos </> sin (j> • 360 (1)
66
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
where <f> is the zenith angle. For the radiation E to the whole sky,
we consequently have :
f 2 r 2
£=360! /<?<£= 360 Rcos<f> sin<W
(2)
\
*
\
-~ II
15
I
//
/
\
/ / /
1
10
\
V\\\'
a
/ / '
/ / '
// ;
\ \ \
\ W
0
/ / 1
\l '
1 '
\ \\
\ \\
\ \\
11 '
1/ '
/
5
\\
\\
III
III
/
11/
\
f
|
'90 60 30 0 30 60 9C
Zenith distance.
Fig. 1 ib.— Radiation to different parts of the sky. Curves I, II: Mt. Whit-
ney, 1913. Water-vapor pressure; 3.6 and 1.5 mm. Hg. Curve dotted,
Bassour, 1912. Water-vapor pressure; 5 mm. Hg. Temperature of instru-
ment higher at Bassour. Compare table IX.
This integration can conveniently be effected in a mechanical way
by measuring the areas given by ( i ) . The curves that represent the
radiation from a horizontal surface to different parts of the sky are
shown in figure 12. The whole areas included between the curves
and the ^-axis must be proportional to the total radiation. In
measuring the areas we must take into consideration the fact that the
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
67
ordinates represent the radiation within a solid angle of 768.60 and
consequently ought to be divided by the same number. The total
radiation calculated in that way, is given in table IX, together with
the total radiation observed under the same conditions. The mean
Zenith distance.
Fig. 12. — Radiation from horizontal surface to different parts of the sky.
difference between the two values is only 0.003, yiz-? less than 2 per
cent. Considering the great difficulty of the observations upon which
the computed value is based, the agreement must be regarded as very
satisfactory. I therefore think we are justified in drawing there-
from the following conclusions :
68
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
I. That there is proportionality between the radiation and the
energy of the current, used for compensation, down to very low values
of both of them.
This is a very important point, as far as the utility of the instru-
ment is concerned. The truth of the statement is clear from the fact
that we can add up small portions observed and get a sum equal to
the total quantity observed.
II. That the way in which the distribution curves have been extra-
polated down to 900 zenith angle must be nearly correct.
III. That the sky must have been very uniform during the time of
observation. If this had not been the case, it would not have been
possible to calculate the total radiation from observations upon a
single vertical circle.
From the diagrams it is to be concluded that the maximum of
radiation from a horizontal surface toward rings of equal angular
Table X
Observer
Homen
Angstrom I1
Angstrom 21
Angstrom 32
Angstrom 4-
Angstrom 52
1 Mt. Whitney (4,420 m.).
0°-22°30'
22°3o'-4S°
45°-67°3o'
6/°3o'-90°
1. 00
o-fo
O.87
0.6l
I. 00
0.98
O.9O
O.74
I. 00
0.98
0.88
O.67
I .00
0.94
0.86
0.60
0.99
0.92
o-75
O.4I
0.97
0.91
0.65
O.23
1. 5
3-6
3.8
S.o
7-1
!Bassour (1,160 m.).
width takes place in a direction that makes an angle of between 35 °
and 450 with the zenith. An increase of the water- vapor density of
the atmosphere shifts this maximum nearer the zenith; with de-
creasing density the maximum approaches a limiting position of 450,
which it would have if no absorbing and radiating atmosphere
existed.
In table X, which is obtained by measuring the corresponding
areas in figure 12, the ratios are given between the values of the
radiation within various zones, obtained from the observations, and
the same values as calculated from the simple sine-cosine law, that is,
for the case where a horizontal surface radiates directly to a non-
absorbing space. Hereby the radiation is assumed to be unity for
zenith angle o°. Between 8o° and 900 the radiation is only between
0.5 per cent and 2.0 per cent of the total radiation. The influence
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 69
of mountain regions that do not rise higher than about 10 or 15
degrees above the horizon is therefore very small and can be neg-
lected. In valley regions the effective radiation must be less than on
a plane, owing to the shading influence of the mountains around.
The conditions will, however, be slightly complicated through the
superposed radiation from the surface of the mountains themselves,
a radiation that is dependent upon the temperature of the heights
and the properties of their surfaces (influence of snow).
CHAPTER VII
RADIATION BETWEEN THE SKY AND THE EARTH DURING THE
DAYTIME
I must include here some observations which, in spite of their pre-
liminary nature, yet may be of use in throwing- a certain light upon
questions nearly connected with the problem especially in view.
In the daytime, the radiation exchange between the sky and the
earth is complicated by the diffuse sky radiation of short wave length
that is present in addition to the temperature radiation of the sky. If
this diffuse radiation is stronger than the effective temperature ra-
diation to the sky, a black body like the instrument will receive heat.
In the contrary case it will lose heat by radiation.
If one attempts to measure this positive (from sky to earth) or
negative radiation with the instrument used in the present investi-
gation, the sun itself being carefully screened off, such an attempt
meets with the difficulty arising from the introduction of a systematic
error. The bright metal strip has a smaller reflecting power for
the diffuse radiation of short wave length than for the longer heat
waves and we can no longer make use of the instrumental constant k,
which holds only for long waves such as we have to deal with in the
measurements of the nocturnal radiation. The reflecting power of
the strips being about 97 per cent for waves longer than 2 fx, and
only about 70 per cent for waves of 0.5 /x length (a mean value of the
wave length of the diffuse sky radiation), the introduction of the
constant k into daylight measurements will evidently give a value
of the sky radiation that is about 30 to 35 per cent too low.
On several occasions during the summer of 1912, I had the
opportunity of making skylight measurements as well with my own
instrument as with an instrument constructed on the same principle,
but modified for the purpose of making day observations. This
latter instrument is briefly described by Abbot and Fowle1 in their
interesting paper, " Volcanoes and Climate," where the effect of
the diffusing power of the atmosphere on the climate is fully dis-
cussed. Both the strips employed in this instrument are blackened.
1 Smithsonian Miscellaneous Collections, Vol. 60, No. 29, 1913. (Reprinted
in Annals of the Astrophysical Observatory of the Smithsonian Institution,
Vol. 3.)
70
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
71
Instead of being side by side, the strips are here placed one above the
other beneath a thin horizontal plate of brass. When the instrument
was in use, a blackened screen was placed beneath it, so that the
lower strip was exchanging- radiation only with this screen, which
subtended a hemisphere. The upper strip was exchanging radiation
with the whole sky. The radiation was calculated from the current
necessary to heat the upper strip to the same temperature as the
lower one.
Even in the use of this instrument in its original form, it is difficult
to avoid some systematic errors. One is due to the difficulty of pro-
tecting the screen with which the lower strip exchanges radiation,
from absorbing a small fraction of the incoming radiation and in this
way giving rise to a heating of the lower strip. And secondly the
convection is apt to be different, the effect of rising air currents being
greater for the upper strip than for the lower one. The error in-
Table XI — Radiation of the Sky
Sept. 5
Sept. 6
Sept. 7
Mean
— 0. 169
■ — O 2GK
— 0.208
+0-047
■ — 0 . 220
+0.26l
— 0. 194
Noon ■
+ 0.062 -4-OOQ2
+O.067
After sunset
—0 . 208
+ 0.250
— 0 . 225
+0.307
- — 0.2l8
Total sky radiation. . .
+O.273
troduced by these causes may possibly amount to 10 or 15 per cent.
In this instrument as well as in the original Angstrom instrument,
the error, when we attempt to measure the sky radiation during the
day, tends to make this radiation appear weaker than it really is.
Table XI gives some results of observations with the last named
instrument, taken by Dr. Abbot and the author. My measurements
of the nocturnal radiation during the preceding and following nights
are given in the same place. The total diffuse sky radiation is calcu-
lated on the assumption that the effective temperature radiation dur-
ing the daytime is a mean of the morning and evening values deter-
mined by the nocturnal apparatus. The sky was perfectly uniform
during the observations but was overcast by a faint yellow-tinted
haze, ascribed by Abbot to the eruption of Mount Katmai in Alaska.
The energy of the direct solar beam at noon was, for all three days,
1.24 to 1.25 cal. The sun's zenith angle at noon was 32 °. From the
table it may be seen that there was always an access of radiation from
the sky, indicating that the diffuse radiation from the sky was always
*J2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
stronger than the outgoing effective temperature radiation. The
same was indicated by the nocturnal instrument, which, on two
different occasions, showed, in one case no appreciable radiation in
any direction, and in the other case a faint positive radiation from
the sky. If we correct for the reflection of the bright strip the two
instruments seem to be in general agreement with each other, show-
ing the radiation from the sky to be positive in the middle of the day,
under the conditions of the place. Lo Surdo found the same to be
the case at Naples, where he observed during some summer days.
On the other hand, Homen's observations at Lojosee in Finland,
show that there the radiation during the daytime had the direction
from earth to sky, and that consequently the effective temperature
radiation was stronger (and very much stronger) than the incoming
diffused light. The observations of the two observers are naturally
in no way contradictory. The total radiation during the daytime is
a function of many variables, which may differ largely from place to
place. It is dependent on the effective temperature radiation to the
sky. This radiation is probably about the same in different lati-
tudes, a circumstance which will be discussed below ; the effect of
the higher temperature in low latitudes being counterbalanced by
a high humidity. Thus we must seek the explanation in the behavior
of the other important term, the scattered skylight. The strength
of this light is dependent upon the diffusing power of the atmosphere :
the molecular scattering and the scattering by dust, smoke, and other
suspended particles in the air. For a not too low transmission of the
air, the intensity of the skylight must increase with a decrease in the
transmission power, so that the skylight is intense when the solar
radiation is feeble, and vice versa.
There is nothing to indicate that the scattering power of the atmos-
phere is larger as a rule in low latitudes than at high ones, and I am
therefore inclined to think that we ought not to ascribe the high
intensity of the skylight in low latitudes to that cause. But the in-
tensity of skylight is affected by another important factor — the
height of the sun above the horizon. The nearer the sun approaches
the zenith, the more intense must be the light reaching us from the
diffusing atmosphere. The theory of scattered skylight, with due
consideration of the so-called " self-illumination " of the sky, has
been treated in a very interesting and remarkable paper by L. V.
King.1 In his paper King gives curves and equations representing
1 Phil. Trans. Roy. Soc. London, Ser. A, Vol. 212, pp. 375-433.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 73
the intensity of the scattered skylight as a function of the attenuation
of the solar radiation and of the zenith distance of the sun. The
theoretical result is not in exact agreement with the few observations
that have been made, for instance, by Abbot and Fowle, which may
be partly due to the difficulties in this kind of observation; but the
theoretical consideration proves that the intensity of the skylight
must be a decreasing function of the sun's zenith distance. For the
same transmission coefficient of the atmosphere, the skylight must
therefore be stronger, on an average, in low latitudes than in high
ones.
Systematic observations on the intensity of skylight in its de-
pendence on other conditions are almost entirely lacking. This is one
of the most important problems in atmospheric optics, whose conse-
quences deeply affect the questions of climate and of the effects of
dust and haze and volcanic eruptions upon the temperature condi-
tions of the earth. The publications of Nichols, Dorno, and especially
those of Abbot and Fowle contain important contributions to the
problem. The outlines for further investigations of the subject seem
to me to be given by the theoretical considerations of King.
A question of special interest for the problem I have dealt with in
my investigation is this: Is the temperature radiation of the atmos-
phere during the day the same as during the night, when temperature
and humidity conditions are assumed to be the same, or will the at-
mosphere under the direct influence of the solar radiation assume
properties which will result in a deviation from the conditions pre-
vailing in the night-time as far as the radiation is concerned ? This
question ought to be treated in a general way by methods allowing
us to eliminate the short wave radiation and to observe the tempera-
ture radiation during different times of the day. Here I will only
give a brief account of some observations made during the total
eclipse of the sun in 1914 and of conclusions to be drawn from them
in regard to the last named question. The observations were carried
out at Aviken, a place situated on the Swedish coast, on the central
line of the total eclipse, during the two nights preceding and one
night following the total eclipse and also during the eclipse itself.
As I myself was engaged in other observations I had availed myself
of the able assistance of Dr. G. Witt and of Mr. E. Welander of the
Institute of Engineering, Stockholm, for carrying out these observa-
tions.
In order to protect the instrument from the direct sunlight, a
screen arrangement was used, where the screen, through a simple
74
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
mechanical device, could be made to follow the changes in the
position of the sun. The screen was blackened on the side turned
towards the instrument and covered with white paper on the other
side. The screen itself was to no appreciable degree heated by the
sun radiation.
In figure 13 the observations are plotted as ordinates in a dia-
gram where the time of the day is given by the abscissae. The more
the sunlight — and therefore also the scattered skylight — is cut off
Fig. 13. — Radiation observed during total eclipse August 20, 1914.
by the shadowing body of the moon, the more the effective radiation
to the sky naturally increases. From what has been said above it is
clear that we are right in comparing the radiation during the total
phase only, with the values obtained during the night. The feeble
radiation from the corona is perfectly negligible and causes no com-
plications. The mean radiation during the totality is found to be
0.160. At the same time the temperature of the surrounding air was
13.60, the humidity as given by the Assmann psychrometer, y.j mm.
A comparison between the value of the effective radiation during the
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 75
eclipse and the value given by night observations under the same
temperature and humidity conditions, displays a very slight differ-
ence. I therefore think that one may conclude that the effective
temperature radiation during the day follows the same laws as hold
for the nocturnal radiation. More extensive investigations are how-
ever needed before this conclusion can be regarded as definite.
It is of interest to notice that during the whole time preceding
the eclipse, the instrument showed an outgoing radiation to the sky.
From the intensity of this radiation it can be concluded that, at least
before noon, the temperature radiation to the sky must have been
stronger than the diffuse radiation from it. The same was found
by Homen to be the case at Lojosee in Finland, as has been indicated
in the discussion above.
CHAPTER VIII
APPLICATIONS TO SOME METEOROLOGICAL PROBLEMS
A. NOCTURNAL RADIATION AT VARIOUS ALTITUDES
The number of investigations contributing to our knowledge of
this special question is not large. When we have mentioned the
simultaneous observations of Pernter1 at Rauris and on Sonnblick,
and the observations of Lo Surdo 2 at Naples and Vesuvius we have
exhausted the previous work on this subject. The observations that
have been described above seem now to give a basis for forming a
general view upon the question of the influence of altitude upon the
effective radiation. In several cases observations have been carried
out simultaneously at different altitudes, but before we enter upon a
comparison between them, we shall treat the subject in a more general
way. As has been emphasized on several occasions, our observations
indicate that the atmospheric radiation in the lower layers of the
atmosphere is dependent chiefly on two variables: temperature and
humidity. Hence it is obvious that if we know the temperature and
the integral humidity as functions of the altitude, we can calculate
the radiation of the atmosphere at different altitudes, provided that
the relation between radiation, temperature, and humidity is also
known. It has been the object of my previous investigations to find
this relation ; hence, if the temperature and humidity at the earth's
surface are known, together with the temperature gradient and the
humidity gradient, I can from these data calculate the radiation at
different altitudes. The radiation of the atmosphere will evidently
always decrease with increasing altitude. But the effective radia-
tion, which is dependent also on the temperature of the radiating
surface, will behave very differently under different conditions. If
no radiating atmosphere existed, the effective radiation would de-
crease with a rise in altitude owing to the decreasing temperature.
If the temperature of the atmosphere were constant, the effective ra-
diation would always increase, when we moved to higher levels,
owing to the fact that the atmosphere (which is now assumed to
radiate) gets thinner the higher the altitude.
1 Loc. cit. (Histor. Survey).
2 Nuovo Cimento, 1900.
76
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
77
In order to get a general idea of the conditions, I will assume that
Suring's formula :
> 2606 V T 20 /
e i, — 6 c
holds for the distribution of the humidity, and that the temperature
gradient is constant up to an altitude of 5,000 m. I will consider
the following special cases :
I The temperature gradient is o.8° per 100 meters.
II
o.6°
The pressure of the aqueous vapor at the earth's surface is: (a)
5 mm.; (b) 10 mm.; (c) 15 mm. g
The effective radiation Rt at different altitudes can then be calcu-
lated according to the formula :
Rt = T4- 0.170 [1 + 1.26- e-°'0G9P] • 10-10
where p can be obtained from Suring's formula, and where en has
to be corrected for the conditions pointed out in chapter V, B, of
this paper. In table XIIa are given, (1) the temperature (t), (2)
Table XIIa — Radiation at Different Altitudes
Altitude
t
en
e, "
n
1
eh"
p'
p"
p'"
R'
R" R'"
0
25°
.s.o
10. 0
15.0
5-5
11. 0
16.6
0.205
O.164 O.146
IOOO
170
3.3s
0.7
10. 0
3-4
6.8
10. 1
0.208
0. 171 0.150
2000
9*
2.15
4.3
6.45
2.05
4.1
6.1
0.205
O.1770. 167
3000
1°
1. 35
2.7
4-05
1-3
2.4
3-0
0.195
O.178 O.165
4000
— r
0.77
1. 55
2.3
0.7
1.2
r.8
O.182
O.175 O.166
5000
—15°
0.46
0.91
1.4
0.34
0.67
1.0
0. 166
0. 161 0.158
Table XIIb — Radiation at Different Altitudes
Altitude
0
IOOO
2000
3000
4000
5000
1
en
en"
en"
p'
p"
/"
R'
,0.205
J
250
5.0
10. 0
15.0
5-5
11. 0
16.6
19°
3.35
6.7
10. 0
3-35
6.7
io.o
0.212
13°
2.15
4-3
6.45
1.9
3-8
5.8
0.219
7°
1.35
2.7
4-05
1.1
2.2
3.2
,0.215
i°
0.77
1.55
2.3
o.55
1.0
1.6
0.208
-5°
0.46
0.91
1-4
0.28
o.55
0.8
0.194
R"
o.io6|o. 146
0.1760. 155
0.192 0.180
0.197J0.183
0.200 0.190
0.190 0.185
the pressure of aqueous vapor (en), (3) the corrected pressure (p)
and, finally, the effective radiation (R) at different altitudes. In
table XIIb the same quantities are given for a temperature gradient
of 0.6° per 100 meters. Figure 14 gives the curves, drawn from
Radiation.
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
79
the computed data, for the effective radiation as a function of the alti-
tude. The curves bring out some interesting facts that deserve
special consideration.
For ordinary values of the humidity, the effective radiation has a
maximum at i to 4 km. altitude.
An increase of the humidity or a decrease of the temperature
gradient shifts this maximum to higher altitudes.
The effective radiation gradient is consequently positive at low
altitudes and negative at high altitudes.
An examination of the observations, made simultaneously at dif-
ferent altitudes, must naturally give a result that is in general accord-
ance with these considerations, which are based upon the experi-
mental investigations.
Table XIIIa
Date
Aug. 2. .
3-.
4x
5x
ox
10. .
II. .
12. .
General mean. .
Mean of (x) . . .
At
0.61
0.57
0.48
0.52
0.59
0.58
0.71
0.58
o.53
Lone Pine
18.3
17.6
IS- 8
17. S
15.6
18.7
IS. 9
21.2
17.6
16.3
H
10. 0
8.0
7.8
6.3
7-7
7-7
5-9
5-1
7.3
7.3
0.141
0.166
0.171
0.191
0.154
0.185
0.189
0.108
0.175
0.172
L. P. Canyon
17.0
17.3
15. 1
12.4
11. 4
14.6
15.6
5-5
4-8
0.203
0.212
0.177
0.164
0.168
0.185
0.193
Mt. Whitney
—1-3
—0.7
+0.6
+ 1.0
—1.4
—3-4
—2.5
—1.4
-1.1
-0.6
H
3.2
2.7
2.4
2.1
3-5
3-0
1.2
1.2
2.4
2.5
O.182
O.182
O.I96
0.188
0.166
0.154
0.I9I
0.193
0.l82
0.179
Table XIITb
Date
At
Indio [0 m.]
Mt. SanGorgonio
[3.500]
O.69
0.6l
t
H
R
t
H
R
23X
24X
26.O
24.7
23.5
12. 1
II. 0
9.6
0.134
O.181
O.172
0.7
2.1
2.5
1.6
O.208
0.217
Mean of (x) . . . .
O.65
24.I
10.3
0.177
1-4
2.1
O.213
In table XIIIa I have collected the data, gained simultaneously
at different altitudes during the Mount Whitney expedition. The
values represent mean values during entire nights. They confirm
the fact, already deduced from more general considerations, that
80 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the effective radiation has a maximum at an altitude of between
1,000 and 4,000 meters. Between 2,500 and 4,400 meters the mean
gradient is generally negative; between 1,200 and 2,500 meters it
generally has a positive sign. From the general discussion and the
curves that represent ideal cases it is probable that the effective radia-
tion always decreases with an increase in altitude, when about 3,000
meters is exceeded. Up to that altitude we shall generally find an
increase of the effective radiation with the height. The latter condi-
tions are demonstrated by my simultaneous observations at Indio
and Mount San Gorgonio (table XIIIb), as well as by Pernter's1
observations at Rauris and on the top of Sonnblick.
B. INFLUENCE OF HAZE AND ATMOSPHERIC DUST UPON THE
NOCTURNAL RADIATION
From the observations made in Algeria, the conclusion was drawn 2
that a slight haziness, indicated by a decrease in the transmission by
the atmosphere of visible rays (clouds not formed), had no appre-
ciable influence upon the radiation of the atmosphere. In fact it was
found from pyrheliometric measurements during the day that the
transmission of the atmosphere generally kept a high or low or
average value during periods of several days, the changes being slow
and continuous from one extreme to the other. The assumption
being made that the nights falling between days of a certain value of
transmission can be classified as showing the same character as the
days, it was found that the nocturnal mean radiation during nights
belonging to a period of high transmission only differed within the
limits of probable error from the mean value obtained during low
transmission periods.3
The observations at Bassour, Algeria, were taken at a time when
the volcanic dust from the eruption of Mt. Katmai at Alaska caused
a considerable decrease in the sun radiation transmitted to the sur-
face of the earth. Several observers, such as Hellmann,4 Abbot and
Fowle,5 Kimball,6 Jensen,7 and others, all agree as regards the prob-
1 Pernter, loc. cit.
2 A. Angstrom: Studies in Nocturnal Radiation, I. Astroph. Journ., June,
I9I3-
3 Abbot and Fowle : Volcanoes and Climate, 1. c, p. 13.
4Zeitschrift fur Meteorologie, Januari, 1913.
5 Volcanoes and Climate. Smithsonian Misc. Collections, Vol. 60, No. 29.
8 Bulletin of the Mount Weather Observatory, Vol. 3, Part 2.
7 S. A. Mitt. d. Vereinigung von Freunden d. Astronomie und kosm.
Physik, 1913.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 8l
able cause of this remarkable haziness. As regards the atmospheric
conditions at Bassour, I may quote the description given by Abbot
and Fowle in their interesting paper, Volcanoes and Climate : " On
June 19 Mr. Abbot began to notice in Bassour streaks resembling
smoke lying along the horizon, as if there were a forest fire in the
neighborhood of the station. These streaks continued all summer,
and were very marked before sunrise and after sunset, covering
the sky towards the sun nearly to the zenith. After a few days
the sky became mottled, especially near the sun. The appearance
was like that of the so-called mackerel sky, although there were
absolutely no clouds. In the months of July, August, and so long
as the expedition remained in September, the sky was very hazy, and
it was found that the intensity of the radiation of the sun was greatly
decreased by uncommonly great haziness." Abbot and Dorno 1 both
agree as to the average decrease per cent in the solar radiation caused
by the dust ; it was found to be about 20 per cent. " In the ultra-violet
and visible spectrum the effect was almost uniform for all wave
lengths, but was somewhat less in the infra-red." (Volcanoes and
Climate.)
It is of very great interest to consider, in connection with the
observations named, the. effect of volcanic dust upon the nocturnal
radiation. Unfortunately the observations at Algeria were not begun
until after the haze had reached a considerable density, and therefore
we cannot compare observations taken at the same place before
and during the dust period. But the observations taken at Lone Pine
during the California expedition may furnish a reliable basis for
comparison, the two stations having almost exactly the same altitude.
If we therefore consider the curve giving the relation between radia-
tion and humidity at Lone Pine in comparison with the same curve
obtained at Bassour, both curves reduced to the same temperature,
we may from this draw some conclusions in regard to the effect of
the volcanic haze. These curves are given in figure 5, and we can
from the diagram read off the departures of the Lone Pine curve
from the curve taken at Bassour. These departures are given in
the following table, together with the mean departure, which is found
to be +0.003 or Just about 2 per cent of the mean radiation. The
Lone Pine values are, on an average, a little less than 2 per cent higher
than the values obtained at Bassour under identical conditions. If
we compare the radiation values at Indio with those at Bassour in
the same way, we shall find a departure of +■§ per cent in favor of
1 Met. Zt., 29, 1912.
82 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the Indio values. One may conclude from this that the volcanic dust,
which causes a decrease of about 40 per cent (Dorno) in the ultra-
violet radiation and about 20 per cent in the visible affects the rays
Effective Radiation
p mm. Lone Pine-Bassour
4 — O.OO4
5 + 0-°°5
6 + 0.012
7 +0.015
8 + 0.009
9 — 0.003
10^
— 0.013
11J
.Mean + 0.003
that constitute the nocturnal radiation less than 2 per cent. As
the nocturnal radiation has probably its maximum of energy in a
region of wave lengths at about 8 /x, this is a fact that in itself is
not very astonishing. Measurements in the sun's energy spectrum
show that even for waves not longer than about 0.8 jx, the trans-
mission of the atmosphere is very nearly equal to unity, the rays
being very slightly affected by changes in the scattering power of the
air. If we use the observations of Abbot or of Dorno in regard to the
weakening of the ultra-violet and visible light, and apply the law of
Rayleigh for the relation between scattering and wave length, we find
from these data, applied to the average wave lengths of the regions
concerned, that about 97 per cent of the radiation at 8 /x must pass
undisturbed by the dust particles. There are several objections against
a quantitative application of the theory of Rayleigh to the conditions
here considered, but at least it shows that our result cannot be re-
garded as unexpected.
The fact that the nocturnal radiation has only decreased by about
2 per cent, when on the other hand the incoming solar radiation is
reduced to about 80 per cent of its former value, explains the inter-
esting relation between climate and volcanic eruptions pointed out
by Abbot and Fowle in their paper already referred to. That the
climatic effect is not larger, in spite of the great decrease in the inso-
lation, may be due to the large number of processes at work — so to
say — tending to balance or to weaken the consequences of a decrease
in the incoming radiation. It has been shown here that this decrease
is not to any appreciable amount counterbalanced by a decrease in the
outgoing radiation from the surface of earth. But there are other
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 83
means by which heat is carried away from the surface, evaporation,
and especially convection, being factors that are not negligible. It
is probable that if a part of the solar radiation is really absorbed by
the volcanic dust, this will tend to diminish the temperature gradient
between the sea level and the upper strata of the atmosphere, and
consequently cause a decrease in the vertical heat convection from
the lower stations. A second access of radiation is due to the scattered
skylight, and Abbot as well as Dorno point out that the sum of sky-
light and direct solar radiation was subjected to only a relatively small
change by the effect of the dust. One has naturally to expect that if
a part of the direct solar radiation is uniformly scattered by the atmos-
phere, a part of the scattered radiation will reach the surface of the
earth in the form of skylight, this part increasing with an increase
in the scattering power. Part of the scattered radiation is reflected
out to space. Similar conditions naturally hold for the nocturnal
radiation, and it is evident that the quantity measured by the instru-
ment will always be the outgoing heat radiation diminished by the
part of this radiation that is reflected back by the diffusing atmos-
phere upon the radiating surface.
C. RADIATION FROM LARGE WATER SURFACES
The radiation from bodies with reflecting but not absorbing or
diffusing surfaces depends upon their reflecting power and their
temperature only. The emission of radiation in a direction that
makes an angle <£ with the normal to the surface at the point con-
sidered, is determined by the relation :
E,/, = €0 ( 1 — Rq )
where c^ is the radiation of a black surface in the direction <f>, and
i?0 the reflected fraction of the light incident in the named direction.
For the total radiation emitted we have
where the integration is to be extended over the whole hemisphere.
In chapter VI, I have given an account of some observations that
show in what way the radiation from a black surface to the sky is
dependent on the direction. As a very large part of the earth's sur-
face is covered with water, and therefore slightly different from the
conditions defined by the " black surface," I have thought it to be of
interest to give here a brief discussion of the case where we have,
instead of the black surface, a plane water surface radiating out to
84
SMITHSONIAN .\ I I si 'i.l .1 VNEOUS COLLECTIONS
VOL.
65
space. The problem is important for the knowledge of the loss of
heat from the oceans, and would probably be worth a special inves-
tigation in connection with an elaborate discussion of the quantity
of heat absorbed from the incoming sun and sky radiation by water
surfaces. Here I propose only to give a short preliminary survey
of the question, giving at the same time the general outlines of the
probable conditions.
15
10
5
15
10'
5
\
c
\
c
—
nl
/
/
90 60 30 0
Zenith distance.
Fig. 15.— Radiation from water surface to sky. Lower curve for water
surface. Upper curve for perfect radiator. From Bassour observations
(p = 5mm.). Ratio of areas 0.937.
In figure 12 I have given some curves representing the relative
radiation from a black surface in various directions toward rings of
equal angular width. The total energy emitted is represented by the
areas of these curves. Now, if every ordinate is multiplied by the
factor (i—Rfj,), where R<j> can be obtained from Fresnel's formulae,
if we know the index of refraction, the area included by the new
curve will give us the radiation emitted by a water surface under the
same conditions of temperature and water-vapor pressure. In figure
15 such curves are given. I have here assumed the mean refrac-
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
85
tive index for the long waves here considered to be 1.33, a value
that is based upon measurements by Rubens and myself. The
upper curve is taken from figure 12, curve IV. This same curve
corresponds to a water-vapor pressure of 5 mm. The ratio between
the areas is 0.937, i. e., the water surface radiates under the given
conditions 93.7 per cent of the radiation from a black body. A
change in the water-vapor pressure will affect this ratio only to a
small extent.
I will now assume that a black horizontal surface radiates to space,
and that the vertical distribution of the water vapor over the surface
satisfies the conditions for which our radiation formula holds (Chap-
ter III (2) ). Then the radiation can be computed provided the tern-
Temperature.
Fig. 16.
perature is known. If the black surface is replaced by a water sur-
face the radiation will be only 94 per cent of its former value. The
latter radiation is given as a function of the temperature by figure
16, where I have applied the considerations made above to the in-
terval between — io° C. and +200 C. From the figure may be seen
how the radiation is kept almost constant through the increase with
rising temperature of the water-vapor content of the atmosphere.
There is only a slight decrease in the radiation with rising tem-
perature.
The ideal conditions here imagined are probably more or less in-
consistent with the actual state of things. In the first place, the air
immediately above the ocean is generally not saturated with water
vapor, the relative humidity being rarely more than about 90 per cent.
In the second place, it is not quite correct to assume that the average
distribution of the water vapor over the ocean is the same as the
#
86 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
average distribution over land. This will give a deviation from the
assumed conditions and consequently a different absolute value to
the radiation, but it will probably only to a small extent change the
relative values and the general form of the curve.
Melloni1 concludes his first memoir on the cooling of bodies ex-
posed to the sky, published about 70 years ago, with the following
remarkable statement, upon which he seems to lay a certain stress :
" . . . . Un corps expose pendant la nuit a Faction d'un ciel egalement
pur et serein se ref roidit toujours de la meme quantite quelle que soit
la temperature de l'air."
One may at first be inclined to attach very little importance to this
statement. It seems in fact to be in contradiction with the most
elementary laws of radiation. If we consider the temperature of the
radiating surface as the only variable upon which the radiation
depends, we would expect the cooling of the body below the tem-
perature of the surroundings to be proportional to the fourth power
of its absolute temperature. At o° C. the cooling would for instance
be only about three fourths as much as at 200 C.
Now the effect of temperature is generally a double one, as far as
the radiation process is concerned. With a rise in temperature there
generally follows an increase in the absolute humidity, which causes
an increase in the radiating power of the atmosphere. The increase
of the temperature radiation from the radiating surface is balanced
by a corresponding increase in the radiation of the atmosphere ; and
the observed effective radiation is therefore only subjected to a small
variation. The observations, discussed in previous chapters, seem
now to indicate that the law of Melloni is approximately true with
the following modification :
The cooling of a body, exposed to radiate to a clear night sky, is
almost independent of the temperature of the surroundings, pro-
vided that the relative humidity keeps a constant value.
This conclusion, which can be drawn from the observations on the
influence of humidity and temperature on the effective radiation,
must be regarded as remarkable. It includes another consequence,
namely, that a high incoming radiation (sky and sun) and a there-
from resulting tendency to an increase of the temperature, is gen-
erally not counterbalanced by a corresponding increase in the
effective radiation from the surface of the earth to space. The vari-
ations of the incoming radiation are therefore, under constant tem-
perature conditions, almost entirely counterbalanced by variations in
convection, and evaporation (or other changes) of water.
1 Melloni, loc. cit. (chapter II).
CONCLUDING REMARKS
In this " Study of the Radiation of the Atmosphere," I have at-
tempted an investigation of the influence of various factors —
humidity, temperature, haze, clouds — upon the radiation of the atmos-
phere. The results of these investigations are briefly summarized at
the beginning of the paper.
It may be of advantage here to state in a few words in what
respects this study must be regarded as incomplete and in need
of further extended investigations. In the first place, it will be
noticed that my observations have been limited to a particular time of
year; the observations in Algeria and in California have all been
made during the periods July-August of the years 1912 and 1913.
Now the investigations, as yet unpublished, carried on at the
Physical Institute of Upsala, indicate that the amount of ozone
contained in the atmosphere is larger in winter time than in summer
time. Further, it has been shown by K. Angstrom 1 that the ozone
has two strong absorption bands, the one at A = 4.8 /x, the other at
A = 9. 1 to 10. ft, of which the latter especially is situated in a region of
the spectrum where the radiation of a black body of the temperature
of the atmosphere ought to have its maximum of radiation. Then
it is obvious that the radiation of the atmosphere must be dependent
also upon the quantity of ozone present. Spectroscopic investiga-
tions indicate that in the summer time the ozone present in the air
is practically nil; it is therefore not liable to have introduced any
complications into the results discussed in this paper. But in the
winter the quantity of ozone is often considerable, and it is not im-
possible that the variations of the effective radiation in the winter
may be partly due to variations in the quantity of ozone in the
upper air layers. The consequence of the higher, radiating power
of the atmosphere, due to the presence of ozone, must be that the
effective radiation ought to be found to be less in the winter than
is to be expected from the observations discussed in this paper.
Another point where it is desirable that the observations of the
" nocturnal radiation " should be extended, is in regard to conditions
under which the quantity of water in the air is very small. Such
1 K. Angstrom : Arkiv fur Mat., Astr. och Fysik I, p. 347, 1904. Ibidem, I, p.
395, 1904.
88 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
observations will not only be more directly comparable with the
observations on high mountains than those used here for such a
comparison, but they will also furnish a basis for studying- the
variations in a dry atmosphere and the influences by which these
variations are affected. Further, the study of the radiation of the
upper air layers is as yet very incomplete and ought to be extended
by means of continuous observations on high mountains or, perhaps
better, from balloons. My observations indicate that the " perfectly
dry atmosphere " has a radiating power as great as 50 per cent of the
radiation of a black body at the temperature of the place of observa-
tion. The upper air layers — the stratosphere — must therefore have
a considerable influence upon the heat economy of the earth as a
whole. Observations at high altitudes of the absorption and radia-
tion of the atmosphere are therefore very desirable.
Finally, means must be found to study the effective radiation
during the daytime in a more systematic way than has been done
in this paper. The effective temperature radiation — that is, the dif-
ference between the total effective radiation and the access of scat-
tered skylight — can evidently be obtained by measuring these two last
named quantities simultaneously ; measurements that do not seem to
involve insurmountable difficulties.
EXPLANATION OF FIGURES 17 TO 25
The figures give the effective radiation in — = — '-. 10 2, plotted as ordinates
cm." mm.
against the time (in hours of the night) as abscissae. The curves are governed
by the observations given in several of the tables, XIV to XX. For the
graphical interpretation I have chosen some of the observations that seem to me
to bring forward, in a marked and evident way, the influence of humidity or
temperature upon the radiation. They therefore represent cases where either
the temperature has been almost constant (as on high mountains), and the
humidity subjected to variations, or where the humidity has been constant and
the temperature has varied.
89
Radiation and temperature.
Radiation and temperature.
Radiation and temperature.
Radiation and temperature.
Radiation and temperature.
Radiation.
Radiation and pressure (mm. Hg.)-
Radiation and pressure (mm. Hg.) '
Radiation and pressure (mm. Hg.)
EXPLANATION OF TABLES XIV TO XXI
In the following tables are included all the observations at Indio (Table
XIV), at Lone Pine (Table XV), at Lone Pine Canyon (Table XVI), at
Mount San Antonio (Table XVII), at Mount San Gorgonio (Table XVIII),
at Mount Whitney (Table XIX), and at Mount Wilson (Table XX). Upon the
values given in these tables, the studies of the total radiation are based. In the
tables are given: (i) the date, (2) the time, (3) the temperature (t), (4) the
pressure of aqueous vapor {H), (5) the radiation of a black body (5"*) at the
temperature (t) (Kurlbaum's constant), (6) the observed effective radiation
(Rt), (7) the difference between St and Rt, here defined as being the radiation
of the atmosphere, (8) this radiation reduced to a temperature of 200 C, in
accordance with the discussion presented in chapter V : B (E 20O ) , and finally
Remarks in regard to the general meteorological conditions prevailing at the
time of observation. With each night of observation is given the initials of the
observers : A. K. Angstrom, E. H. Kennard, F. P. Brackett, R. D. Williams,
and W. Brewster.
99
IOO
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table XIV
Place: Indio. Altitude: o m. B = 760 mm. Instrument No. 17
Date
Time
1
H
st
Rt
st-Rt
•ca20
Remarks
July 22
7:50
26.6
13.59
0.618
0.123
0.495
0.453 A. K. A. Cloudless
8:40
24.9
13.67
0.604
0.118
0.486
0.455 sky, wind W.,
10:00
28.3
12.24
0.632
0. 129
0.503
0.451 calm.
10:15
27-5
11.86
0.625
0.143
0.482
0.436
11 :oo
27.8
11 • 43
0.628
0.147
0.481
0.433
12: 10
1 :oo
26. 1
26.4
10.87
11. 13
0.616
0. 140
0.476
0.438
2:15
25.8
10.64
0.611
0.140
0.471
0.436
3:45
23.6
10.77
0.593
0.133
0.460
0.440
4:30
22.8
10.67
0.587
0.136
0.451
0.435
July 23
7:50
29.5
11-33
0.642
0.193
0.449
0.396
A. K. A. Sky per-
9:00
28.1
11.30
0.630
0.193
0.437
0.391 fectly cloudless
10:15
25.2
11.56
0.606
0.182
0.424
0.394 calm.
11:05
24.7
11. 41
0.602
0.181
0.421
0.396:
12:45
23.6
10.47
0.593
0. 172
0.421
0.402
2:15
23-3
10.52
0.591
0.178
0.413
0.397
3:30
22.2
10.52
0.582
0.175
0.407
0.395
4:25
21.0
10.82
0.572
0. 171
0.401
0.396
July 24
7:45
29-5
9.65
0.642
0.183
0.459
0.404IW B. Skyperfect-
9:00
27-5
9-30
0.625
0.183
0.442
0.399 ly cloudless, calm.
10:05
25.0
10.97
0.605
0.166
0.439
0.410,
11:15
23.9
10.69
0.596
0.169
0.427
0.405
12:10
23.0
10.31
0.588
0. 169
0.419
0.402
1:05
23.0
9-37
0.588
0.173
0.415
0.398
2:00
21.2
9.65
0.573
0.170
0.403
0-397
3:10
21.2
8.81
0.573
0.174
0.399
0-393
4:05
20.6
8.43
0.568
0.172
0.396
0.393
4:20
19-5
8.15
0.560
0.163
0.397
0.400
Table XV
Place: Lone Pine. Altitude: 1,140 m. B = 650 mm. Instrument No. 18
Aug. 2
9:25
18. 1
10. 11
0.548
o.i45
0.403
0.415
F. P. B., R. D. W.
10:00
19.4
8.99
0-559
0.144
0.415
0.419
Cloudless, calm.
11:05
17.4
9.7i
0.543
0.127
0.416
0.433
12:10
21.3
10.20
0.575
0.149
0.426
0.420
1:05
18.2
10.58
0.548
0.134
0.414
0.426
2:00
18. 1
10.50
0-547
0.136
0.411
0.423
3:30
17.5
10.24
0.544
0. 141
0.403
0.419
4.00
16.7
10.01
0.538
0.151
0.387
0.407
Aug. 3
8:00
20.0
8.44
0.564
o.i75
0.389
0.389
R. D. W., F. P. B.
9:00
22.5
7-47
0.584
0.172
0.412
0-399
Cloudless, calm.
10:00
21 .1
8.00
0.572
0.182
0.390
0.384
11:00
18.8
8.28
0.554
0.173
0.381
0.389
12:00
17.8
7.07
0.546
o.i74
0.372
0.385
1:00
15.2
8.54
0.527
0.139
0.388
0.415
2:25
16.8
7-73
0.538
0. 169
0.369
0.386
3:00
13.0
8.47
0.512
0.168
0-344
0.379
4:00
13.4
8.29
0.514
0.147
0.367
0.402
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
IOI
Table XV — Continued
Place: Lone Pine. Altitude: 1,140 m. B = 650 mm. Instrument No. 18
Date
Time
*
H
st
Rt
St-Rt
P
Remarks
Aug. 4
10:07
19.9
8.43
0.563
0.169
0.394
0-395
F. P. B. Cloudless,
ll:00
19.0
7
oS
0.556
0.167
0.389
0.395
calm.
12:00
17-3
9
01
0.542
0.183
0.359
0-374
R. D. W. Radiation
i :oo
13.2
8
39
0.513
0. 170
0.343
0.376 variable.
2:05
12.7
7
59
O.509
0.167
0.342
0.378
3:05
15.0
6
99
0.525
0.154
0.371
0-397
4:05
13.3
6
90
0.514
0.189
0.325
0.356
Aug. 5
8:15
24.6
5
87
0.602
0.212
0.390
0.366
R. D. W., F. P. B.
9:05
23.0
5
79
0.588
0.215
0.373
0.358
Radiation fluctu-
10:00
17. 1
7
38
0.541
0.195
0.346
0.360
ating.
11:00
21.4
5
46
0-575
0.205
0.370
0.363
12:00
15.6
6
33
0.530 0.191
0.339
0.359
1:05
12.4
6
96
0.507
0. 166
0.341
0.378
2:05
14.8
5
97
O.524
0.189
0.335
0.360
3:05
14.4
6
52
0.521
0 174
0.347
0.375
4:05
14.4
5
96
O.521
0.170
o.35i
0.379
Aug. 9
8:00
21. 1
7
99
0.572
0. 180
0.392
0.387
R. D. W., F. P. B.
9:00
22.4
7
18
0.583
0.177
0.406
0.394 Hazy in the even-
10:00
18.8
8
29
0.554
0.168
0.386
0-394
ing, per f ectly
11:00
16.9
7
61
0.540
0.163
0.377
0.394
cloudless.
12:00
14.6
8
03
0.523
0.143
0.380
0.408
1 :oo
12.7
8
13
0.509
0.142
0.367
0.406
. 2:00
12.2
8
11
0.506
0.139
0.367
0.407
3:05
10.7
5
42
0.496
0.139
0.357
0.405
4:00
10.6
8
39
0.495
0.133
0.362
0.411
Aug. 10
8:20
21.9
7
12
0.579
0.196
0.383
0.374
E. H. K. Few scat-
9:00
22.0
7
25
0.580
0.211
0.369
0.360 tered clouds at N.
9:10
10:10
0.202
0.378
0.378
0.368 horizon in the
0.373: evening. Perfect-
21. 1
7
38
0.572
0.194
10:20
0.197
0.209
0.375
0.362
0.370; ly cloudless after
0.359 9:00.
11:00
20.9
7
48
0.571
11 : 10
0.199
0.195
0.372
0.369
0.371
12:05
19.8
7
61
0.562
0.367
12:15
1:00
0.201
0.361
0.370
0.365
0.387
16.9
8
05
0.540
0.170
3:05
16.4
8
23
0.536
-0-159
0.377
0.389
3:i5
16.4
8
23
0.536
0. 162
0.374
0.393
4:30
12.7
8
01
0.510
0.154
0.356
0.393
4:40
8:25
0.510
0.147
0.189
0.363
0.400
Aug. 11
20.5
6
40
0.568
0.379
0.377
E. H. K. Perfectly
9:00
J24.6
6.12-f
0.602
0.197
0.405
0.381
cloudless. Breezy.
9:10
0.602
0.223
0.379
0.356
10:00 "\„„ „
10:10 IK2
5-78{
0.590
0.204
0.386
0.371
0.590
0.204
0.386
0.371
II:00l)20.7
11 : 101 J '
5.3*{
0.569
0.202
0.367
0.363
0.569
0.207
0.362
0.358
s;a}*-»
6.59{
0.555
0.204
0.351
0.358
0.555
0.210
0.345
0.352
i;?s}'4.3
6.18-f
0.521
0.189
0.332
0.359
0.521
0.176
0.345
0.372
2:00
2: 10
j-12.0
5-78{
0.505
0.505
0.190
0.176
0.315
0.329
0.351
0.365
102
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table XV — Continued
Place: Lone Pine. Altitude: 1,140 m. B = 650 mm. Instrument No. 18
Date
Time
H
S
R*
St-R,
E,
Re-marks
Aug. II
Aug. 12
Aug. 14
5:00 8.9
7:00
7:20
7:25
7:45
8:00
8:10
8:35
9-.ooH
9:10 J
10:00
10:10
11:15
11:25
12:00
12:10
1:00
1:10
2:05
2:20
3:05
3:15
25.6
6. 27 1
5.36{
5-i6{
5-37
7-3i
25.2
23.9
20.6
j-26.0
}
}
}i8.7
}20.5
}20.5
}i5.7
}i5.6
5.56
4-7i{
:20 23.4
:25
:50 21.3
4.49>[
5.30^
5-o8{
3.85{
3.67{
5-26[
5-9i{
7-52
4.69
0.502
0.502
0.490
0.490
0.491
0.491
0.484
0.610
0.610
0.606
0.606
0.613
0.613
0.613
0.596
0.596
0.568
0.568
0.553
0.553
0.568
0.568
0.568
0.5
0.530
0.530
0.529
0.529
0.592
0.592
0.574
0.196
0.155
0.187
0.180
0.173
0.156
0.171
0.208
0.212
0.209
0.211
0.199
0.220
0.218
0.209
0.220
0.195
0.197
0.197
0.208
0.1
0.220
0.192
0.184
0.172
0.163
0. 169
0.154
0.241
0.231
0.231
0.306
0.347
0.303
0.310
0.318
0.335
0.313
0.402
0.398
0.397
0.395
0.414
0.393
0-395
0.387
0.376
0.373
0.371
0.356
0.345
0.379
0.348
0.376
0.3
0.358
0.367
0.360
0.375
o.35i
0.361
0.343
0.343
0.384
0.349
0.356
0.364
0.385
0.365
0.372
0.369
0.369
0.367
0.381
0.362
0.369
0.368
0.357
0.371
0.369
0.363
0.352
0.377
0.346
0.374
0.382
0.380
0.389
0.382
0-397
0.337
0.347
0.338
E. H. K. Perfectly
cloudless, fluctua-
tions.
E. H. K. Perfectly
cloudless, windy.
A. K. A. Very clear
Table XVI
Place : Lone Pine Canyon. Altitude : 2,500 m. B
! mm. Instrument No. 22
Aug. 4
8:05
18.9
4-7i
0.555
0.203
0.352
0.359
W.
B.
Cloudless.
4: 10
15.0
5.27
0.526
0.203
0.323
0.346
Aug. 5
8:05
18.9
5-32
0.555
0.211
0.344
0.351
w.
B.
Cloudless.
9:00
18.9
2-54
0.555
0.199
0.356
0.363
10:05
18.6
2.65
0.553
0.226
0.327
0.334
11:00
18.6
3.24
0.553
0.220
0.333
0.340
12:00
16. 1
4.00
0.533
0.218
0.315
0.333
1 :oo
16. 1
3-75
0.533
0.217
0.316
0.334
2:10
16.7
4.07
0.538
0.209
0.329
0.345
2:55
16.8
3-53
0.539
0.194
0.345
0.361
3:55
15.0
4-23
0.526
0.214
0.312
0.334
Aug. 8
9:35
15.5
7-63
0.529
0. 176
0.353
0.376
w.
B.
Cloudless.
10:00
14.7
6.30
0.523
0.177
0.346
0.372
Aug. 9
8:15
12.8
7-34
0.510
0.184
0.326
0.359
w.
B.
Cloudless.
9:10
12.2
5. 98
0.506
0.161
0.345
0.383
10:00
12.2
.5.98
0.506
0.158
0.348
0.386
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
IO3
Table XVI — Continued
Place : Lone Pine Canyon. Altitude : 2,500 m. B = <
I mm. Instrument No. 22
Date
Time
t
H
^t
*t
St~Rt
■^020
Remarks
Aug. 9
10:55
12.5
6.09
0.508
0.154
0-354
0.391
W. B. Hazy but
12:00
12.8
5-52
0.510
O.169
0.341
0-375
cloudless.
i :oo
11. 9
5.88
0.504
0. 169
0.335
0.374
2:00
12.8
5.i8
0.508
0.l6l
0.347
0.382
3:00
12.0
5.04
0.505
O.169
0.336
0.375
3:55
12.0
5-04
0.505
O.I47
0.358
0.397
Aug. 10
9:i5
12.2
5-93
0.506
O.166
0.340
0.378JW. B. Breezy,
0 367 cloudless.
3:10
10.6
6.53
0.495
O.172
O.323
4:00
10.6
6.06
0.495
0.168
O.327
0.371
Table XVII
Place : Mt. San Antonio. Altitude : 3,000 m. B = 532 mm. Instrument No. 22
July 12
July 13
8:00
8:05
9:05
10:05
11:00
12:00
12:05
1 :oo
1 :io
2:00
2:10
'3:00
3:10
4:05
7:10
7:30
8:30
8:50
9:45
10:50
12:30
2:15
4:i5
11. 8
11. 2
10.7
10.8
11. 2
10. 0
11. 3
9-7
10. 0
18.3
3-91
17.9
3-63
17-5
16.9
3-23
6.35
16.7
7.85
16.6
9-55
16.4
16.2
6.48
8.10
2.46
2.60
2.22
2.36
1.99
2.27
I.63
2.l6
2.27
0.550
0.550
0-547
0.547
0.544
0.539
0.539
0.538
0.538
0.537
0.537
0.536
0.534
0.534
0.503
0.499
O.496
O.496
O.499
0.491
0.500
O.489
0.491
0.202
0.209
0.209
0.202
0.200
0.193
0.203
O.I99
O.189
0.188
O.187
0.195
0.I3I
O.164
0.203
0.I9I
0.213
0.220
0.2II
0.219
0.225
0.220
0.221
0.348
O.34I
0.338
0-345
0-344
O.346
0.336
0.339
0-349
0-349
0.350
0.341
O.403
0.370
0.300
O.308
O.283
O.276
O.288
0.272
0.275
O.269
O.270
0.357
0.350
0.348
0.355
0.357
0.362
0.352
0.356
0.366
0.366
0.367
0.358
A. K. A. Perfectly
cloudless, windy.
0.335
0.346
0.321
0.312
0.324
0.313
0.309
0.310
0.310
Clouds after 3:00.
A. K. A. Hazy at
N. horizon, cloud-
less.
Table XVIII
Place : Mt. San Gorgonio. Altitude : 3,500 m. B = 495 mm. Instrument No. 22
July 23
July 24
8:00
9:00
10:20
11 :oo
12:05
1 :20
2:00
3:00
4:00
8:20
9:00
10:00
11:00
12:00
2.0
1.1
1.3
0.9
0.9
0.4
0.2
0.0
-0.6
2.8
2.3
2.2
1.6
1.8
2-95
2.66
2
"6l
I
80
2
21
I
91
I
54
1.88
1. 14
0.438
0.432
0.433
0.431
0.431
0.428
0.426
0.425
0.421
0.443
0.440
0.439
0.435
0.436
0.204
0.215
0.215
0.205
0.207
0.208
0.208
0.208
0. 198
0.2II
0.215
0.215
0.223
0.221
0.234
0.217
0.2l8
0.226
0 224
0.220
0.2l8
0.217
0.223
0.232
0.225
0.224
0.212
0.215
0.300
0.282
O.283
O.294
O.292
0.290
0.288
0.288
O.299
0.295
O.289
O.287
0.274
O.276
E. H. K. After
stormy and rainy
day perfectly
cloudless night.
F. P. B. Perfectly
cloudless.
104
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table XIX
Place: Mt. Whitney. Altitude: 4,420 m. B=446 mm. Instrument No. 17
Date
Aug. 1
Aug. 2
Aug. 3
Aug. 4
Aug. S
Time
11
R.
\St-Rt\ Ea20
Remarks
11 :oo — 2.9
9:40 — 0.8
11:45—1.4
1:05—1.4
2:05—1.9
3:35—Li
7:30 0
8:05 0.3
9:05—0.1
10:10
11:00 — 0. 1
12:05—0
1 : 00 — 0
2: 10 — 1
3:25—1
4:10;— 1
4:25
4:351—1.6
4:45
5:00—1.7
8:05
8:25
9:00
9:10
10:00
10:10
11:00
11:10
12:00
12:10
1 :oo
1 :io
2:15
2:30
3:00
3:10
3:20
3:30
4:00
4:10
7:10
7:40
8:05
8:10
9:00
9:10
10:00
10:45
11:00
11 :io
12:00
12:10
1.4
1.3
1. 1
0.6
"o.'<5
'0.6
0.0
0.0
1.9
1.3
3.70 0.407 o.u
3.23 0.420
3.81 0.416
3.79 0.416
3.61 0.413
1.68 0.418
3-75
3.30
3.80
3.18
3.15
2.97
2.90
1.70
1.40
1.76
1.73
3.28
2.59
2.39
2.46
2.42
2.44
2.32
2.00
1-93
2.21
0.425
0.413
0.424
0.424
0.424
0.422
0.421
0.418
0.418
0.417
0.417
0.415
0.415
0.414
0.434
0-434
0.433
0.433
0.432
0.432
0.429
0.429
0.429
0.429
0.429
0.429
0.425
0.42S
0.426
0.426
0.425
0.425
0.425
0.425
0.176
0.165
0.183
0. 160
0.226
0.194
0.207
0.217
0.170
0.177
0. 160
0.171
0.163
0.167
0.183
0.179
0.182
0.190
0.183
0.195
0.199
0.193
0.195
0.190
0.194
0.194
0.189
0.188
0.188
0.180
o. 182
0.179
0.184
0.213
0.228
0.200
0.210
0.202
0.223
0.218 0.302 E. H. K. Cloudless
only about 11:00.
0.244 0.327'A. K. A. Cloudless
0.251 0.345! after cloudy and
0.233 0.320! windy evening.
0.253 0.343!
0.192! 0.260
0.2311 0.306E. H. K. Perfectly
o.2o6| 0.271 cloudless, balloon
0.207] 0.277 sent up, calm.
0.254 0.338}
2.67!
0.437 0.179
0.437 0.190
2.87; 0.4361 0.182
2.74
1 .1
2.06
1. 1
1.83
0.6
1 .90
0.436!
0.4331
0.433
0.432
0.432I
0.432J
0.432,
0.429
0.429
0.247
0.262
0.250
0.255!
0.251
0.234
0.238
0.233
0.225
0.231
0.239
0.235
0.240
0.238
0.242
0.238
0.235
0.240
0.241
0.241
0.249
0.247
0.246
0.241
0.213
0.198
0.225
0.215
0.223
0.202
0.258
0.247
0.254
189 0.247
191 1 0.242
200 0.233
0.244
0.257
0.237
0.233
0.232
188
175
0.195
p. 199
0.197
0.108
0.329
0.350
0.335
0.344
0.339
0.316
0.321
0.317
0.306
0.314
0.310
0.304
0.311
0.308
0.315
0.309
0.308
0.314
0.315
0.315
0.327
0.324
0.326
0.319
0.281
0.262
0.298
0.285
0.295
0.267
0.332
0.317
0.326
0.317
0.313
0.302
0.317
0.334
0.308
0.303
0.304
0.231 0.303
A. K. A. Perfectly
cloudless, balloon
up, calm.
E. H. K. Balloon
up, breezy after
10:00.
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
I05
Table XIX — Continued
Place: Mt. Whitney. Altitude: 4,420 m. B = 442 mm. Instrument No. 17
Date
Time
H
•t
R
S+-R<
Remarks
Aug. 5
Aug. 8
Aug. 9
Aug. 11
Aug. 12
1:10
1:20
2: 10
2:20
3:00
3:05
4:0s
4:20
9:45
10:00
10:35
10.55
12:30
12:45
2:30
4:35
4:45
8:10
8:20
9:05
9:45
■ 9:55
11 :io
12:55
1 : 10
2:55
3:i5
4:i5
4:20
8:00
8:10
0.3
0.6
1. 81
0.3
1.32
0.6
1.52
—1.3
3-59
—1.4
3-35
—3-0
3.51
-3-6
—3-7
3.07
2.46
— 2.2
2.37
-2.3
-2.4
-2.7
-3.0
-2.6
-2.5
0.427
0.427
0.429
0.429
0.427
0.427
0.429
0.429
0.417
0.417
0.416
0.416
0.407
0.407
0.403
0.402
0.402
0.412
0.412
0.411
0.410
0.410
0.409
0.407
0.407
0.409
0.409
0.54 0.410
0.410
o. 185J 0.242
0.192, 0.235
0.191 0.238
0.198' 0.231
0.181 0.246
0.187; 0.240
0.173 0.256
0.176 0.253
1.47
1.47
I .12
1.02
O.69
—1.4
I. 17
O.416
O.416
0.173
O.162
o. 167
0.161
0.150
0.154
0.152
0. 160
0. 161
0.201
0.l8l
0.221
O.I96
O.183
0.179
0. 172
O.174
0. 191
0.189
0.193
0.194
0.194
0. 192
0.244
0.255
0.249
0.255
0.257
0.253
0.251
0.242
0.241
0.2II
0.231
0. 190
0.214
0.227
0.230
0.235
0.233
0.218
0.220
0.217
0.2l6
0.222
0.224
0.318
0.309
0.312
0.302
0.323
O.316
0.335
0.332
0.330
0.344
0.337
0.345
0.356
0.351
0.351
0.338
0.337
O.289
O.316
O.260
0.293
0.3II
O.316
0.325
0.322
0.300
0.303
O.298
O.297
0.300
0.303
E. H. K. Perfectly
cloudless
A. K. A. Cloudless
after 9:30.
A. K. A. Cloudless
after foggy after-
noon.
A. K. A. Cloudless
after clear day.
Radiation vari-
able.
A. K. A. Clouds
after 8:30.
Table XX
Place: Mt. Wilson. Altitude: 1,730m. B = 6i5mm. Instrument No. 17
Aug. 27
9.10
9:25
10:00
10:20
11:00
11 :io
12:00
12:10
12:55
1:05
18.9
12.37
18.8
18.5
18.3
II
II
10
45
34
92
18.2
10
97
18.4
II
13
17.8
II
• 17
17.8
II
04
18.5
10
69
0.555
0.555
0.554
0.552
0.550
0.550
0.549
0.549
0.551
0.551
0.546
0.546
0.546
0.546
0.552
0.552
0.143
0. 140
0.147
0.152
0.150
0.151
0.149
0.151
0.145
0. 146
0.141
0.141
0.147
0.147
0.155
0.154
0.412
0.415
0.407
0.400
0.400
0.399
0.400
0.398
0.406
0.405
0.405
0.405
0.399
0.399
0.397
0.398
0.420
0.423
0.415
0.410
0.411
0.410
0.412
0.410
0.416
0.41S
0.419
0.419
0.413
0.413
0.407
0.408
A. K. A. Calm and
perfectly cloud-
less night.
io6
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
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APPENDIX I
FREE-AIR DATA IN SOUTHERN CALIFORNIA, JULY AND
AUGUST, 19131
By the Aerial Section, U. S. Weather Bureau — Wm. R. Blair in Charge
[Dated, Mount Weather, Va., May 26, 1914]
The Astrophysical Observatory of the Smithsonian Institution, and the
Mount Weather Observatory of the Weather Bureau co-operating during July
and August, 1913, made observations in southern California : (a) Of solar
radiation at high levels, by means of a photographically recording pyrhe-
liometer, carried by free balloons; (b) of the total moisture content of the
air above Mount Wilson, by means of the spectroscope; (c) of nocturnal radia-
tion, by means of the K. Angstrom compensation apparatus; (d) of the
meteorological elements, air pressure, temperature, humidity, and movement,
at different altitudes by means of meteorographs, carried by free balloons at
Avalon, and by captive balloons at Lone Pine and at the summit of Mount
Whitney. The pyrheliometric observations have already been discussed by
C. G. Abbot in Science, March 6, 1914. It is the purpose of this present paper
to communicate more particularly the meteorological observations.
A. The Free Balloon Observations
Morning and evening ascensions were made on July 23 and 24, 1913, and
thereafter daily ascensions until August 12, 1913 — 23 ascensions in all. When
a pyrheliometer was taken up, in addition to the meteorograph, the ascension
for the day was so timed that the highest point would be reached about noon.
On other days the ascensions were made shortly after sunrise or just before
sunset. Table 1 shows the number of balloons recovered, their landing
points, and other information of general interest.
Table i. — Statistics of sounding balloon flights from Avalon, Cal., during
July and August, 1913
Date
Hoi
Balloons
U
Ascen-
B
3
sional
force
55
Kg.
2
2
0.8
2
0.8
2
0.9
2
1.1
2
1.2
2
1.0
2
1.6
2
1.4
2
1-3
2
0.9
2
0.8
2
0.8
2
0.9
2
0.9
Landing point
Hori-
zontal
dis-
tance
trav-
eled
Direc-
tion
trav-
eled
High-
est
alti-
tude
reach-
ed
Lowest
tem-
pera-
ture
record-
ed
1913
July 23
24
26
27
28
29
30
a 31
Aug. 1
2
3
5
7
6: 06 a . .
5: i3 P •
5: 11 p .
4=S7P •
5 : 05 P •
11 : 10 a
10: 54 a ,
10: 37 a
10: 36 a .
10: 59 a ,
5:o7p .,
5:o7p.
4: 52 P ••
5:23 P •■
4:43P ■•
Huntington Beach, Cal.
Armada, Cal
San Diego, Cal
Oceanside, Cal
Chi no, Cal
Los Angeles, Cal
Atmore's Ranch, Cal
Los Pasos Hills, Cal....
New Hall, Cal
Inglewood, Cal
Downey, Cal
Fullerton, Cal
Colton, Cal
Baldwin Park, Cal
Pacific Ocean
Km.
42
122
131
91
97
80
140
122
128
72
70
75
120
97
4
NE.
ENE.
ESE.
E.
NE.
N.
NNW.
NNW.
N.
N.
N.
NNE.
NE.
NNE.
NW.
M.
25,160
20,389
°C.
-56
— ss
23,870
19,485
23,066
32,643
22,294
23,466
21,302
17,428
-64
-62
—60
—53
-58
-58
-67
-67
6,442
14,100
1,976
-25
—43
19
1 Reprinted by permission from the Monthly Weather Review, July, 1914,
pp. 410-426.
8 !07
io8
SMITHSONIAN MISCELLANEOUS COLLECTIONS
VOL. 6-
All free balloons were started at Avalon, Santa Catalina Island, Cal.
Because of the possibility of the instrument coming down in the ocean,
balloons were sent up in pairs and with a float. This float weighed approxi-
mately 450 grams. Each balloon was filled until it would lift decidedly
everything to be sent up except the float The balloons were then attached
to the system in such a way that when either of them burst it would detach
itself from the system, which then sank to the earth's surface with the
remaining balloon. This device by which the balloons are connected with
Fig. I. — Device for releasing burst balloon.
the system and which serves the purpose of releasing the burst balloon is
shown in figure 1. It is made of spring brass wire of approximately 2.4 mm.
diameter. The pressure of the springs B and C on the wire A at the points
D and E is sufficient to prevent the rings from slipping off in case cord F or G
becomes slack. The weight of the burst balloon or of what is left of it slips
the ring off easily. Cords F and G must be so short that they will not twist
above the device.
The balloons used v/ere of thick rubber, similar to those used at Huron in
the early autumn of 1910 and at Fort Omaha in the late winter of 191 1, but
not so large. They were filled with electrolytic hydrogen which had been
compressed in steel cylinders.
bo
a
c
3
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SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
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no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
III
The highest ascension of the series was made on July 30. This exceeds
the previous highest ascension from this continent by more than two kilo-
meters. The record obtained in this ascension is shown in figure 2.
In seven of the ascensions from which records were returned the instrument
was carried to an altitude of 18 or more kilometers above sea level. The
temperatures recorded and the ascensional rates of the balloons have been
Alt.
k m
Alt.
k m
/
18
17
f
17
16
15
f
16
15
14
f"
\
- —
14
13
f-
13
12
U
10
U
10
1
9
8
9
8
1
6
5
4
3
2
5
4
3
2 3 4 5
-50° -40° -30° -20° -10° 0° 10° 20°
A5E ENS ZONAL RATE.mps.
TEMPERATl/RC. 0EEREE5 EENT/GRAOE. A
Fig. 3. — Relation between ascensional rates of balloons and air temperatures.
averaged and compared in table 2 and in figure 3. The mean of the
observed temperatures in the seven ascensions does not show a minimum of
temperature below the 18-kilometer level. The mean of the ascensional rates
of the balloons shows, in general, an increase with altitude. Above the 18-
kilometer level the individual ascensions show a decrease in the ascensional
rates of the balloons soon after the minimum of temperature has been passed
through. This relation between the air temperature and the ascensional rate of
112 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the balloons is similar to that already found. (See Bulletin Mount Weather
Observatory, Washington, 191 1, 4: 186.) It indicates that, in addition to the
known factors entering into the ascensional rate of any balloon, there is the
unknown factor of the difference in temperature between the gas in the balloon
and the air through which the balloon is passing. While the temperature
distribution in the free air is in general known, it would be impossible to
predict, with sufficient accuracy for a particular ascension, the point of maxi-
mum ascensional rate or minor variations in the rate. On the other hand,
careful observation of the ascensional rate of a free, sealed, rubber balloon
might indicate fairly well the peculiarities of the temperature distribution at
the time of the ascension. In this connection the author calls attention to an
entirely erroneous statement in Bulletin of the Mount Weather Observatory,
4:186, regarding the adiabatic cooling of hydrogen gas. The approximate
rate of cooling per kilometer came in some way to be considered the rate to
the 15-kilometer level. The statement based on this error should not have
appeared, nor is it needed to account for the observed peculiarities in the
ascensional rate of free rubber balloons under consideration.
The instruments used were the same as those used in previous series of
soundings. The calibration of the instruments was similar to that for pre-
vious series, except that the pressure and temperature elements were calibrated
in a smaller chamber in which ventilation and temperature were under some-
what better control and in which temperatures down to — 6o° C. could easily
be obtained. (See Bulletin Mount Weather Observatory, Washington, 191 1,
4:187.)
The data obtained in each ascension are presented in table 4 with inter-
polations at the 500-meter intervals up to 5 kilometers above sea level, and at
i-kilometer intervals above the 5-kilometer level. In figure 4 a diagram of
the temperature-altitude relation is shown for each observation. Figure 5
shows the mean value of this relation for the period. The free air isotherms
for the period are shown in figure 6. The horizontal projections of the
balloon paths, as far as they could be observed, are shown in figure 7. Only
one theodolite was used, the altitudes being computed from the observed
air pressures.
An inversion of temperature, with the maximum temperature somewhere
between the x/t- and 2-kilometer levels, is shown in each curve of figure 4.
This inversion of temperature is found, whether the observation be made in
the morning, near noon, or in the late afternoon. It does not seem to accom-
pany any particular wind direction. A similar inversion of temperature was
observed in most of the ascensions made at Indianapolis, Fort Omaha, and
Huron.
As shown in figure 5, the altitude at which the mean temperature for the
period is a minimum is 17 kilometers. The minimum temperature observed
in any ascension may be more than a kilometer above or below the height of
this mean. In two ascensions, those of the 23d and 27th of July, the change
of temperature with altitude begins to decrease at about the 8-kilometer level,
while in the ascensions of August 2 and 3 this change does not take place
until the 12-kilometer level. The temperature change from day to day is best
shown in figure 6. The lowest temperature observed, — 67.50 C, was at about
the 16.5-kilometer level on August 3. About the same temperature had been
observed at the 16-kilometer level on the day before.
Alt
k m
—
1
/
/
/
\
1EER
:es
CENl
\
0° 1
}° 2
0° J
)° 4
0° E
0°
\
\
-
\22.0°
AIL.
i m
-60 -50 -40 -80 -20 -10 0 10 20
Fig. 5.- — Curve showing mean temperature gradient at Avalon, Cal., July 23-
August 3, 1913.
Il6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM
117
u8
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
A comparison of the curve shown in figure 5 with that shown in the Bulletin
of the Mount Weather Observatory, 4 : 302, figure 31, shows the surface
temperature indicated in figure 5 higher by 6.40 C, the minimum temperature
lower by 3.50 C, the maximum next above this minimum less than 2° C.
lower than the corresponding values shown in figure 31. The minimum tem-
perature shown in figure 5 occurs at an altitude higher by 1.5 kilometers than
that shown in figure 31. The maximum temperature next above the minimum
AUG. 7.
AUG.E.
0n>
'l5347
wJUl.ET^
\123'23ir
jt2387Cta
V.
Fig. 9. — Horizontal projections of the paths of the sounding balloons liberated
at Avalon, Cal., July 23-August 10, 1913.
temperature is shown at about the same altitude in both curves. The curves
have the same general appearance. That shown in figure 5 represents summer
conditions at latitude 330 N. That shown in figure 31 represents conditions
in all seasons, to some extent, the late summer and early autumn being better
represented than the other seasons, at about latitude 400 N.
The variations of humidity with altitude and from day to day are rather
closely related to the variations of temperature. In table 3 the absolute
humidities observed have been assembled and a mean shown.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
119
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0
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b
<
0
V
a
a
■a
120
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table 4. — Results of sounding balloon ascensions, Avalon, Cal.
July 23, 1913.
Time
Alti-
tude
Pres-
sure
Tem-
pera-
ture
At
Humidity
Wind
Rel. Abs. i Direction
Vel.
Remarks
/;. m.
6 06.0
6 08.0
6 09.1
6 10.2
6 12.2
6 17.4
6 18.9
6 24. 5
6 24.8
6 31.7
6 36.4
6 42.9
6 so. 4
7 00.4
7 08.3
7 iS-i
7 26. i
•7 43-9
7 Si. 5
7 S4-2|
7 57-7;
8 10.9
'&"ik'.'3
8 31.8,
8 33-7
M.
34
489
500
737
1,000
1,032
1. 454
1,500
2,000
2,500
2,784
3,000
3.194
3.5oo
4,000
4.500
4,719
4,818
5,000
6,000
6.793
7,000
8,000
8,184
9,000
10,000
10,289
11,000
12,000
12,584
13,000
14,000
15,000
15,092
16,000
17,000
17,379
18,000
19,000
19,983
20,000
21,000
22,000
23,000
24,000
25,000
25,160
25,000
24,000
23,045
23,000
22,000
21,000
20,314
20,000
19,000
18,411
18,000
17,857
17,254
17,000
16,000
15,000
14,285
14,000
13,000
12,603
12,000
11,000
10,000
9,855
9,536
9,000
Mm.
759-5
719.8
699.0
675.0
642.3
547-5
520.8
430 . 1
424.7
143-9
69.2
46.1
60.0
65.3
71.7
112. 3
144.3
214. s
224.9
°C.
i9-3
i4-3
14. 1
12.4
18.5
18.9
17-1
16.8
12.6
8-5
6-3
5-5
4-9
2-5
- 1.0
- 4.6
- 6.1
- 6.6
- 7-9
- 14.7
—20.0
—21.6
—29.1
-30.5
-34-3
-38.8
-39-9
—41.4
-43-4
-44.6
-46.5
—50.6
-54-8
-55-2
-55-8
-56.6
-56.9
-56.7
-S6.4
-56.1
-56.1
-53-6
-51-2
-48.7
-46.3
-43-8
—43-4
—43-0
—42.1
-41. 1
—41.2
—42.6
—44.2
-45-1
—46.4
-50.5
-52.8
—50.7
—50.0
—52.1
-Si-*
—Si. 1
—50.4
-49-8
-48.6
— 44-5
—43-0
—41-5
-38.8
—36.4
—36.0
— 37 ->7
—33-5
I.I
"o'.k
-0.5
0.8
P. ct.
77
83
-2.2
0-4
0.8
0.7
o-S
0.8
59
57
49
49
5i
53
54
48
43
40
36
33
31
31
31
29
27
27
25
25
25
25
25
24
23
2.291
1.608
1. 106
0.919
0.882
0.793
0.415
0.241
0.207
0.09s
0.082
0.055
0.034
0.030
0.024
0.019
0.016
0.013
0.008
0.004
0.004
0.004
0.003
0.003
0.003
0.004
0.004
0.004
0.006
0.007
0.010
0.014
0.018
0.019
0.020
0.020
0.021
0.021
0.017
0.013
O.OII
0.010
0.006
0.005
0.006
0.007
0.005
0.006
0.006
0.007
20 O.O08
20 0.009
O.OlS
0.021
0.030
0.041
O.O42
0.035
0.055
g./m? j
12.651 ,
10. in N. 480 W
10.109 N. 47° W
9.972 N. 17° W
9.248
9-147
7.068
6.942
5-597
4-495
3-975
3-354
M.p.s.
1.1
1.1
1.0
10/10 S. NNW.
In base of clouds. In-
version.
Inversion.
Inversion.
Inversion.
Inversion.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
121
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued
July 23, 1913 — Continued
Time
Alti-
tude
Pres-
sure
Tem-
pera-
ture
M
Humidity
Rel. Abs.
Wind
Direction Vel
Remarks
h. mi.
8 37-9
8 44-3
8 50.0
8" 56*9
M.
8,667
8,000
7,456
7,000
6,384
6,000
5,038
5,000
4,500
4,000
3,794
Mm.
254.2
300.3
346.9
483.6
°C.
-31-0
-25.8
-21.6
-19.4
-16.4
-13-8
- 7-7
- 7.4
- 4.0
- a. ,7
0.6
0.6
P. cl.
23
25
27
28
29
30
32
32
32
32
3^
l./m.3
0.071
0.129
0.207
0.265
0-359
0.464
0.832
0.852
1. 126
1.464
1. 612
M.p.s-
July 24, 1913
A. M
5 13.8
5 15-0
5
18. 1
5
5
18.8
20.1
5
5
21.3
23-9
5
29.0
5
33-5
5
5
37-8
38.3
5
42.1
5
48.2
S
5
48.8
53-i
5
58.5
6
05.2
6
6
08.9
i5-i
6
6
18.3
20.0
6
6
21.6
24.0
6
28.7
6
32.8
6
6
36.6
38.7
6
42.4
6
6
45-2
48.0
6
53-3
6 57.0
34
290
500
858
1,000
1,005
1,220
1,500
1,507
1,925
2,000
2,500
2,984
3 , 000
3,5oo
3,907
4,000
4,Soo
4,759
4,853
5,000
5,588
6,000
6,968
7,000
7,"4
7,999
8,000
9,000
9>i7i
0,000
0,423
1,000
1, 016
1,894
2,000
2,464
2,902
3,000
3,206
3,7"
4,000
4,7i6
5,000
5,297
6,000
6.453
6,795
7,000
7,763
8,000
8,207
8,5n
9,000
9,619
20,000
20,389
759-7
737-3
677-4
660.3
638.1
607.5
534-9
■477.8'
429.8
424.7
386.9
323-4
317.0
281.8
240.2
201.6
185.3
163.5
150.3
140.7
134-5
124.9
107.6
"'98's'
82.3
78-3
67.6
63.1
60.2
50.8
45-1
20.1
17.7
IS- 8
13-0
14.6
14.6
13-7
16.3
16. 4
15- 1
14.7
11. 4
8-3
8.1
5-2
2.8
2.4
- 0.5
" 1-9
- 1.9
- 2.8
- 6.2
" 9-3
-16.3
-16.3
-16.3
-20.8
-20.8
-26.3
-27-3
-31.7
-34.0
-38.2
-38.3
-41.8
-42.4
-45.1
-45-1
-45-5
-46.1
-46.0
-46.6
-47-9
-49.6
-5i-3
-52.2
-52.8
-55-i
"55-4
-55-8
-55-6
-55-i
"54-8
-53-2
-5i-4
-50.8
-50.1
0.9
'o.&
-1.1
0.4
-0.9
0.3
0.6
0.0
0.6
0.7
0.0
0.5
0.6
0.5
0.7
0.4
0.6
0.0
0.3
0.0
0.2
'o!o"'
0.1
0.7
-0.1
-0.1
-0.3
-0.2
11-363
10.315
9.740
7-398
7.562
7.608
5-243
4-993
3-871
3-015
2.976
2.329
1.870
1.820
1. 441
1 .249
1.249
1 .162
0.852
0.03s
0.034
0.024
0.023
0.016
0.016
0.016
0.014
0.014
0.013
0.012
0.010
0.008
0.007
0.006
0.005
0.004
0.004
0.004
0.005
0.005
0.006
0.009
0.008
0.009
SW
S. 260 w.
S. 49° W.
N. 83°W.
S. 68' W.
S.67° W.
S. 76' W.
S. 31° w.
S. 30° VV.
S. 29° W.
S. 29° W.
S. 25° W.
S. 22° W.
S. 22°' W.
S. 37° W.
S. 49° w.
S. 49° W.
S. 48° w.
S. 48° w.
S. 41° w.
S. 44° W.
S. 58° w.
S. 58° w.
S. 58° w.
S. 60° w.
S. 66° W.
S. 62° W.
S.62° W.
S. 63° W.
S. 63° W.
S. 72° w.
S. 77° W.
S. 72" W.
S. 72° w.
S. 70° W.
S. 73° w.
S. 84° W.
S. 63° w.
S. 63° w.
S. 63° w.
S. 63- w.
S. 59° W.
S. 47° W.
S. 54" W.
S. 61° W.
S. 48° W.
S-39°W.
S. 57° W.
S. 40° W.
S. 22° E-.
S. 74° E..
N.6o° E..
S. 85° E..
S. 75° E..
S. 63° E...
S. 4°E..
S. 57° W.
4.8
6-4
7.6
8.0
12.8
16.
13-
4-
25.
25-
24.
24.
24.
24.
23.
23.
19.
18.
16.
22.
20.
16. 1
18.2
18.4
18.8
15-7
12.3
Few S. Cu. SW.
Inversion.
Inversion.
Few S. Cu. SW.
Inversion.
Few S. Cu. SW.
Balloons disappeared.
122
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table 4. — Results of sounding ballooti ascensions, Avalon, Cal. — Continued
July 27, 1913
Time
Alti-
tude
Pres-
sure
Tem-
pera-
ture
St
Humidity
Wind
Rel. Abs. Direction Vel.
Remarks
p. M.
h. m.
4 57-5
5
00.3
5
5
02.3
04.2
S
07.0'
5
09.0
5
13-0
5
15-0
5
20.5
5
5
25.0
26.1
5
5
30-0
32. 0!
5
38.9
5
46.O
5
5
56.6
59-5
6
6
07-3
09.7
6
20.6
6
28.5
6
35-4
6
41-5
6
44-3
6
45-4
6
49.0
6
51. 1
6
7
57-9
00.0
1
7
03.1
7
09.0
7
11. 9
M.
34
500
704
1,000
1,087
1,388
1,500
1,912
2,000
2,263
2,500
2,980
3,000
3,395
3,500
4,000
4,454
4,Soo
5,ooo
5,292
5,5io
6,000
6,422
6,853
7,000
8,000
8,361
9,000
9,905
10,000
11,000
12,000
12,029
12,369
13,000
14,000
14,080
i4,54i
15,000
16,000
17,000
17,051
18,000
i8,797
19,000
20,000
21,000
21,506
22,000
23,000
23,870
23,000
22, 179
22,000
21,821
21,000
20,229
20,000
19,098
19,000
18,000
17,000
16,916
16,284
16,000
15,228
15,000
14,178
14,000
13,498
13,000
Mm.
759-2
669.9
646.3
607.0
'581*8'
°C.
532.8
505-9
442.6
396-5
385.2
340-8
321.5
259-9
206.6
149-3
141. 8
108.4
101.0
67-7
51.4
33-5
23.0
29.7
3i-3
40.2
48.0
67.9
75-3
k'g.o
105.3
"7-5
-0.8
-0.1
0.8
0-5
o'8|
0.5
'0*8*!
0.9
0.2
0.9
0.5
0.4
-0.3
0.1
0.5
0.1
-0.3
-0.1
1.0
-0.4
-0.2
0.0
-0.4
-0.2
0.1
0.2
0.2
g-/tnfl
11.949
9.687
8.786
8.708
8.507
7-775
7.288
5-504
5.003
3.661
2.852
1. 661
1. 661
I-35I
1 -301
1.064
0.860
0.839
0.581
0.478
0.425
0.289
0.206
0.133
0.118
0.040
0.027
0.017
0.010
0.009
0.006
0.003
0.003
0.004
0.003
0.003
0.003
0.002
0.002
0.001
0.001
0.001
0.002
0.003
0.003
0.003
0.003
0.004
0.004
0.005
0.006
0.005
0.004
0.005
0.007
0.005
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.002
S. 86° W.
S.8o° W.
S. 77° W.
S.47°E..
S. 83° E..
N.410 W.
N.440 w.
N.560 w.
N.8/° W.
S. i'E..
S
S. 3°W.
S. 7°W.
N.850 W.
N.86c W.
S.89°W.
S.85°W.
S.8s°W.
S. 83° W.
S. 82° W.
S. 78" w.
S. 75° W.
S.73°W.
S. 85° W.
S. 81° W.
S. 50° W.
S.390 W.
S. 57° W.
S. 83" w.
S. 83° w.
S.820 w.
S. 820 W.
S.82° W.
N.870 W.
S. 83° W.
S. 67° W.
S. 66° W.
N.740 W.
N.8i°W.
S. 83° W.
S. 68° W.
S. 67" W.
S. 2°W.
M.p.
3
S. 53°
S. 5ic
S 400
S. 30°
S.25°
S. 36°
S. 59'
!.??■:....
N.8o°E..
S. 88° E..
S. 76° E..
S. 88° E..
N.8o°E..
N.77"E..
N.67°E..
N.7o°E..
S. 84° E..
S. 57° E..
S. 55° E..
S. 34° E..
W
N.45°W.
N.58° W.
S. 76° W.
S. 77° W.
S. 79° W.
S. 60° W.
9 2/10S. Cu. WSW.
5 Inversion.
0.8
3-
5-
5-
6.
6.
8.2
8-3
8.4
8.7
I
16.3
16.4 Inversion.
2/10 S. Cu. WSW.
9-
9-
7-
7-
7-
6.
6.8 Inversion.
6.2
5-7
5-3
3-6
1.9
Balloon burst.
Inversion.
Inversion.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
123
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued
July 27, 1913 — Continued
Time
Alti-
tude
Pres-
sure
Tem-
pera-
ture
At
Humidity
Rel. Abs.
Wind
Direction \ Vel.
Remarks
M.
12,734
12,323
12,000
II,8ol
",355
11,000
10,587
10,000
9,000
8,602
8,000
7,034
7,000
6,443
6,184
6,000
5,000
4,615
4,500
4,og4
4,000
3,733
3,5oo
3,000
2,980
2,733
2,500
2,132
2,000
i,977
Mm.
132.4
i4i-4
153-2
164.7
248.5
310.3
336.6
348.7
431.6
461.8
484.0
532.3
548.5
590-7
602.2
°C.
-60.4
-60.4
-60.4
-60.2
-58.5
-56.2
-53-6
-49.1
-41.6
-38.6
-35-0
-29.4
-29.4
-28.6
-26.9
-26.0
-20.8
-18.8
-16.6
- 8.6
- 7-8
- 5-4
- 3-4
1.1
1.4
2.5
4.1
6.8
6-3
6.2
0.0
0.0
0.4
0.6
0.8
0.6
0.1
0.7
o.S
2.0
0.9
0.9
0.4
0.7
P. ct.
y./m3.
0.002
0.002
0.002
0.002
0.003
0.004
0.005
0.010
0.023
0.033
0.049
0.092
0.092
0.117
0.143
0.167
0.347
0.460
0.548
0.991
1. 057
1.224
I-44I
1. 981
2.021
2.234
2.549
3-"8
3.607
3.656
M.p.s.
S. 50° W.. 8.2
S. 62° W. . 10. 0
Balloons disappeared.
July 28, 19 1 3
P. M.
5 05.0
5 06.8
5
5
08.7
10. 0
5
5
5
10.9
11. 4
12.3
5
5
13.8
15-2
5
20.3
5
22.9
5
27.4
5
31.6
5
37-1
S
40.7
5
44-7
5
50.6
5
55-2
6 00.8
34
371
500
787
962
1,000
1,117
1,218
1,377
1,500
1,648
1,923
2,000
2,500
3,000
3,048
3,5oo
3,535
4,000
4,498
5,000
S,4o6
6,000
6,659
7,000
7,478
8,000
8,279
9,000
9,533
10,000
io,399
1 1 , 000
ii,593
759-7
730-3
694.9
680.5
667.8
659-9
647-4
627.1
607.1
53o.i
499.1
442.6
394-3
334-6
299-3
268.2
223.9
197-3
165.2
20.6
iS-8
14.5
11. 7
10.4
10. 1
9-7
15.0
16.2
16.2
16.2
i5.4
14.8
10. o
5-4
5-0
3-o
3-o
0.0
- 2.8
- 5-8
-18. 1
-21.4
-26.3
-30.7
"33-0
-37-8
-41-5
-44-7
-47.2
-50.6
-53-6
1.0
0.7
0.5
"5-2
-0.8
0.0
0.3
0.9
0.4
'o!<5
"o'.6
'o!8
1.0
'o'.8
0.7
0.7
0.5
.813
•073
• 755
.991
• 036
2.429
2.366
1.480
1 .421
1. 015
0.698
0.516
0.403
0.272
0.171
0.125
0.078
0.051
0.040
0.023
0.014
0.010
.005
.003
S
S. 160 W.
S. 33° W.
S. 68° W.
N.670 W.
3-7
3-0
1-5
0.6
9/10 S. Cu. WNW.
In base of S. Cu.
Inversion.
124
SMITHSONIAN MISCELLANEOUS COLLECTIONS
VOL.
65
Table 4. — Results of sounding balloon ascensions, Avalon, Col. — Continued
July 28, 1913 — Continued
Time
Tem-
pera-
ture
At
Humidity
Wind
Rel.
Abs. Direction
Vel.
Remarks
p. M.
h. m.
6 09.3
6 11. 3
6 15-5
M. Mm.
12,000
12,233 I 149.5
13,000 I
13,096 I 131 .0
13,293 I 127. I
14,000 j
14,084 112. 6
19,485 48.1
19,000
18,010 60.5
18,000
17,000 :
16,489 I 77-i
16,063 82.4
16,000 !
15,000
14.253 I 109.6
"C.
-55.7
-56.8
-56.0
-55.7
-55.4
-55 7
-55-7
-56.9
-57-5
-58.8
-58.8
-61.4
-62.6
-62.4
-62.2
-60.1
-58.5
\P. ct.'g./m.3
-0.1
-0.2
0.0
-0.1
0.0
0.2
14
0.003
14
0.002
14
0.003
14
0.003
13
0.003
13
0.003
13
0.003
13
0.002
13
0.002
13
0.002
13
0.002
12
0.001
12
0.001
12
0.001
12
0.001
13
0.001
13
0.002
M.p.s.
Inversion.
Clock stopped at in-
tervals. Time es-
timated.
Clock stopped, but
started again at
highest altitude.
Inversion.
July 29, 1913
II
II. 3
II
II
13-3
14.8
II
16.5
II
18.4
II
20.2
II
22.9
II
25.7
II
28.6
II
II
29.9
33-3
II
II
II
35-0
36.1
37-4
II
II
39-2
41.0
II
43-2
II 45.0
11 45-7
11 46. 8;
11 47.9
11 48.i1
11 49-4
11 53- Oj
11 53.8i
11 53-9
34
418
500
1,000
1,012
i,330
i,5oo
1,684
2,000
2,182
2,500
2,625
3,000
3,344
3,500
4,000
4,041
4,5oo
4,832
5,000
5,120
5,953
6,000
6,272
6.629
6,908
7,000
7,437
7,882
8,000
8,570
9,000
9,029
9,268
9,467
9,707
9,928
10,000
10,248
10,633
io,747
io,794
760.5
726.8
677.0
651.6
624.4
588.3
*557.8'
5H-4
424.8
409-5
367-6
352.7
336.2
324-5
301.7
283.7
257-7
241.7
233-6
226.9
218.9
212.2
202.8
191-3
188.2
186.5
11 55-o 10,915 183.3
1*11,000 I
469.4
18.6
IS. 2
14-5
10.6
10.4
9.4
11. 2
12.7
12.2
11. 9
11. 4
11. 3
93
7-4
6.1
2.2
1.8
- 2.9
- 6.2
- 6.2
- 6.1
-13-4
-13.4
-14.2
-18.9
-19.7
-20.4
-23.7
-27.8
-28.6
"33-2
-36.4
-36.7
-38.2
-39.1
-42.5
-42.1
-43-4
-47.2
-46.9
-47-3
-48.3
-48.7
-49-3
0.8
0.3
-0.9
0.2
0.1
0.5
-0.3
0.9
0-3
1-3
0-3
0.8
0.9
0.8
0.8
0.6
0.5
1.4
-0.2
1.6
-0.8
0.4
2.1
9-933
9-393
9-372
8- 913
8.713
7.645
6.073
4-7II
3.888
3-056
2.733
1.964
1.423
1. 163
0.674
0.601
0.384
0.265
0.265
0.267
0.112
0.112
0.119
0.069
0.064
0.060
0.032
0.021
0.019
0.015
0.011
0.010
0.010
0.009
0.006
0.007
0.006
0.003
N.S6°
N.85°
N.8o°
N.48°
N.47°
2.5
2.5
2.3
1-3
1.2
9/10 S. Cu. NW.
Balloon disappeared
in S. Cu. Inversion.
Inversion.
Inversion.
f Inversion. Onebal-
| loon burst and was
[ detached; remain-
i ingballoonhadsuf-
[ ficient lifting force
to continue ascent.
Clock stopped.
' Estimated by extrapolation from the ascent.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
125
Table 4. — Results of sounding .balloon ascensions, Avalon, Cal. — Continued
July 29, 1913 — Continued
Alti-
tude
Pres-
sure
At
Humidity
Wind
Time
pera-
ture
Rel.
Abs.
Direction
Vel.
Remarks
100 m.
A. M.
h. m.
M.
*23,o66
23,000
22,000
21,305
21,000
20,000
19,000
18,111
18,000
17,145
17,000
16,141
16,000
15,000
14.344
Mm.
27.8
36-3
°C.
—0.4
P. ct.
g./m.s
M.p.s.
-44
-49
-53
-53
5
5
0
5
2
7
4
3
5
7
4
2
2
3
3
6
3
3
3
4
—0.2
i -56
0.0
69-5
81.4
-58
-58
-58
-60
—fin
—0.2
O.I
' -59
107.9 i -58
1 — sR
O.I
0.0
3
3
3
3
3
4
5
0.001
0.001
0.001
0.001
0.001
0.001
0.002
12,386 146.6 —57
11,368 i 170.9 —57
f Balloon burst; clock started running, but times of this and succeeding levels unknown.
July 30, 1913
54-o
57-0
II
II
01. 0
03.0
11 06 . 0
II 07.3
II
II
12.3
13-9
15.0
16.9
18.9
20.0
II
II
26.O
29.O
II
II
37-o
39-0
II
II
45-0
49-3
II
II
53-o
55-5
II
p
12
58.5
M.
01. 0
12
09.0
12 l6.0
12 17.0
12 l8.8
34
362
500'
69s
884
1,000
1,184
1,338
1,500
1,766
1,927
2,000
2,045
2,l85
2,413
2,499
2,500
3,000
3,067
3,339
3.5oo
4,000
4,133
4,362
4.5oo
5,ooo
5,157
5,749
6,000
6,273
6,672
7,000
7.093
7,475
8,000
8,915
9,000
10,000
10,322
10,521
10,832
760.0
731-7
703.8
688.3
664.5
65-J-7
621. 1
609.5
601.3
591-5
576-7
570-3
532.9
516.7
470.1
457-3
414.9
385-4
360.8
342.7
324.5
309.1
255-1
210.3
204.6
195-7
23.0
21.0
19.9
18.3
16.9
18.2
19.9
20.4
20.7
21.3
20.7
20.3
20.2
19.6
20.4
20.1
20.0
18.5
18.3
16. 1
14.8
11. o
10.2
8.2
7-2
3.8
2.7
-I.I
- 3-5
- 6.1
- 9.2
- 9.8
- 9.9
-12.2
-15-9
-22.1
-22.8
-30.2
-32.6
-32.4
-35-6
0.6
0.8
0.7
-1.0
-0.3
-0.2
0.4
o-4
0.4
-0.4
0.3
o-3
0.8
0.7
0.9
0.7
0.6
1.0
0.8
0.2
0.6
0.7
0.7
-0.1
1.0
61
12.415
67
12.155
70
11. 913
74
11.463
80
11.402
69
10.625
54
9.190
40
7.008
36
6.418
2Q
5-353
26
4-636
34
5.922
3«
6.581
45
7.525
30
5.256
24
4.132
24
4.108
IS
2.351
14
2.169
11
1.494
11
1. 381
10
0.993
10
0.945
10
0.832
10
0.780
0.687
0.697
0.399
0.330
0.296
0.230
0.219
0.217
0.142
0.103
0.051
0.048
0.020
0.0l6
0.0l6
0.012
NE
SE
S
S. 500 W
S. 56° W
S. i'W
S. 86°W
S. 42° E
S
S. 32
S. 42
S. 38
S. 35
S- 33
S. 32
S. 33 -
S- 33° E
S.25°E
S. 24° E
S. 14° E
S. 140 E
S. i6°E
S. 16° E
S. 18° E
. 38° E
Few Cu.
8 I I
nversion.
Inversion.
Balloon disappeared.
Few Cu.
Inversion.
126
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued.
July 30, 1913 — Continued
Time
Alti-
tude
Pres-
sure
Tem-
pera-
ture
At
100m.
Humidity
Wind
Rcl.
Abs. ; Direction Vel.
Remarks
P. M.
h. m.
12 25-3
12 26.8
13 37-0
12 37-8;
12 42.3
12 47.2
12 50.1
12 53-7
01.8,
03-9
20.5
I 24.9
(•)
M.
11,000
11,724
12,000
12,391
12,653
13,000
14,000
14,021
15,000
15,241
15,435
16,000
16,707
17,000
18,000
18,263
18,877
19,000
20,000
20,131
21,000
22,000
23,000
23,005
23,932
24,000
25,000
26,000
27,000
28,000
28,062
29,000
30,000
31,000
32,000
32,643
32,000
31,000
30,000
29,000
28 , 000
27,000
26,000
25,118
25,000
24,000
23,000
22,249
22,000
21,000
20,000
19,051
19,000
18,000
17,000
16,160
16,000
Mm.
172.1
156. 1
150.2
122.5
102. 1
99-3
81.8
64.7
58.9
3i-5
27-3
°C.
"37-3
-43-6
-44.2
-44-9
-48.4
-49.1
-51.3
-51-3
-49.2
-48.6
-5i-4
-50.3
-49.0
-49-8
-53-o
-53-9
-50.5
-50.7
-52.3
-52.5
-5i-4
-50.2
-49.0
-49.0
-49-5
-49.4
-47-7
-46.2
-44-5
-42.8
-42.7
-42-5
-42.4
-42.1
-41.9
-41.8
-42.1
-42.9
-43-4
-44.0
-44-7
-45-4
-46.0
-46.6
-46.8
-49.4
-50.8
-52.3
-52.4
-52.6
-53-o
-53-3
-53-2
-52.4
-51-5
-50.8
-50.6
-0.1
0.1
0.2
1-3
-0.2
1.4
0.3
-0.6
P. ct.
\ i
■ 6
6
6
6
6
6
6
6
6
6
6
6
6
6
5
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
6
5
5
5
5
5
3
5
5
5
5
5
5
5
5
5
5
6
6
6
g./mfi
0.010
0.005
0.004
0.004
0.003
0.003
0.002
0.002
0.003
0.003
0.002
0.002
0.003
0.002
0.002
0.001
0.002
0.002
0.001
0.001
0.002
0.002
0.002
0.002
0.002
0.002
0.003
0.004
0.004
0.005
0.005
0.005
0.005
0.006
0.006
0.006
0.006
0.005
0.004
O.OO4
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.002
0.002
0.002
M.f.s.
Inversion.
Inversion.
Inversion.
Inversion.
Inversion.
* Clock stopped at intervals; times of this and subsequent levels unknown.
July 31, 1913
A. M.
10 37.5
34
388
5oo
62a
799
762.0
731-3
711. 5
696.9
22. Q
l8.0
I8.0
18. I
20.5
1.4
0.0
—1.4
64
74*
74
74
63
12.952
11. 261
11. 261
11.328
1 1. 102
5/10 Ci. S.
10 39.3
10 40.2
10 41.0
S.6g°E...
i.5
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
127
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued
July 31, 1913 — Continued
Time
Alti-
tude
Pres-
sure
Tern- At
pera-
ture
Humidity
Rel. Abs.
Wind
Direction Vel
Remarks
A. M.
h. m.
10 41.I
10
43-2
10
45-6
10
47-3
10
48.3
10
S0.2
10
52.0
10
54-5
10
II
57-3
00.2
II
03.0
II
06.0
II
II
09.0
10. 0
II
13.8
II
18.2
II
II
21.2
22.6
II
II
23-9
2S.4
II
II
II
29.6
30.1
3i-3
II
31.8
II
34-8
II
36.4
II
II
40.3
41-5
M.
995
1,000
1.403
1,500
1,898
2,000
2,354
2,500
2,542
3,000
3,109
3.5oo
3,588
4,000
4.418
4.5oo
5,000
5,041
5,795
6,000
6,557
7,000
7.430
8,000
8,384
9,000
10,000
10,188
11,000
",72s
12,000
13,000
13,165
13.533
14,000
14,154
14,646
15,000
16,000
16,166
16,600
i6,933
17,000
i7,i34
18,000
18,607
19,000
19,580
20,000
21,000
21,352
21,557
22,000
22,194
Mm.
681.2
649.7
613.4
58i.4
568.6
531-7
501.7
456.2
4195
381.0
345-2
307.0
269.1
254.9
208.4
166.0
132.9
126.0
114. 2
106.0
K3-7
78.1
74-4
72.0
57-i
49.1
37-4
36.2
32.5
°C.
21.7
21.6
21.7
21.0
19.2
18.7
17.0
17.0
17.0
12.8
12.0
S.I
5.8
3-7
2.7
- i.'S
- 1.8
- 9-3
-H-3
-16.7
-20.6
-24.4
-28.6
-31-3
-32.8
-34-6
-42.2
-43-6
-47-4
-Si- 1
-52.3
-56.9
-57-6
-58.5
-56.7
-56.1
-54-5
-55-4
-57-7
-58.1
-58.8
-58. 4
-58.6
-58.9
-58.0
-57-6
-56.4
-54-6
-53-7
-51.9
-51.2
-51.3
-49.8
-48.6
-0.6
0.9
"o!8
0.9
1.0
0.9
0.7
0.4
0.8
0.5
0.2
-0.4
-0.3
0.2
0.2
P. ct.
46
46
28
26
16
15
g./m.3
8.690
8.640
5.289
4-717
2.613
2-379
1-434
1-434
1-434
1.444
1-375
1. 210
1. 158
0.855
0.620
0.580
0-344
0.336
0.205
0.193
0.145
0.118
0.094
0.062
0.048
0.041
0.034
0.014
0.012
0.007
0.005
0.004
0.002
0.002
0.002
0.002
0.004
0.003
0.003
0.002
0.002
0.001
0.002
0.001
0.001
0.002
0.002
0.002
0.003
0.003
O.OO4
0.004
0.004
0.005
0.006
E...
E...
E...
E..,
E...
E...
E...
E...
E..
E..
E...
E..
E...
K...
E...
E...
E...
E...
E...
E..,
E...
E..
E...
E..
E...
M.p.
5
5
6
6
5
5
8.5
15.0
14.6
12.8
12.7
7
6
9
2
7
4
6
Balloons disappeared
in Cirrus clouds.
5/io Ci. S.
Inversion.
Inversion.
Inversion.
Inversion.
August i, 1913
A. M.
10 36.0
10 36.8
10 38.0
34
179
365
761.0
748.4
732.4
23-9
7i
74
66
15.210
12.667
12.980
12.077
10,137
4/10 Ci. S.
2-7
—1-3
22.4
23.1
24.4
59
46
10 40.0
707
704.1
-0.6
S. 8°W..
0.5
10 40.9
859
691.8
24.7
—0.2
44
9.862
S. 440 E. ..
2.6
1,000
24.2
43
9-369
S.39°|...
6.6
10 41.9
1,015
679.6
24.2
0.3
42
9-I5I
S.38°E...
7-3
l,5oo
22.0
42
8.072
S. 420 E...
8.1
128
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued
August 1, 1913 — Continued
Time
Alti-
tude
Pres-
sure
Tem-
pera-
At
Humidity
Rel. Abs.
Wind
Direction Vel
Remarks
A. M.
h. m
10 44-9
10 5i-i
10 58.8
11 00.7
II
II
II
II
09.8
10.4
II. 2
12.8
II
I4.9
II
I9.2
II
29-3
II
34-5
II
II
36.0
37-2
II
II
40 8
42.7
II
45-2
11
n
53-9
55-2
11
S7-o
12
00.0
p
12
M.
03-3
12 06.0
12 06.7
12 07.2
12 II. 3
12 12.6
12 15.6
12 I7.7|
12 18. 7,
12 I9.3
12 23.O
12 25.3
M.
1. 534
2,000
2,500
2,555
3,000
3.5oo
4,000
4,238
4,432
4,5oo
5,000
5,38i
6,000
6,233
6,296
6,426
6,880
7,000
7,218
8,000
8,138
9,000
10,000
10,703
11,000
1 1 , 966
12,000
12,366
12,827
13,000
13,650
13,977
14,000
14,778
15,000
16,000
16,717
16,849
17,000
17,493
18,000
i8,395
19,000
19,993
20,000
20,195
20,451
20,675
21,000
22,000
23,000
23,466
23,000
22,792
22,000
21,226
21,000
20,000
19,666
19,273
I9,i33
19,000
18,592
18,000
17,483
17,054
17,000
i6,773
Mm.
640.0
567.8
468.7
4Si. 7
400.9
359-7
356.7
350.6
330.7
315.8
279.1
194.6
161. 7
152.5
142. 1
125.4
119. 4
106.0
78.7
77.1
69.7
*6o!o"
47-3
45-7
44.1
42.6
27.7
'30.8
49-8
52.9
54-i
58.8
69.8
74.6
°C.
21.8
18.3
14.6
14.0
10.9
7-4
3-6
2.2
1.9
1-5
- 1.6
- 4.0
" 9-5
-ii. 6
-10.8
-13-7
-16.8
-17-5
-18.2
-23.5
-24-3
-30.0
-36.6
-41.4
-43-2
-49-5
-49.4
-49-8
-52.4
-52.3
-52.4
-49.8
-49.8
-49.8
-50.5
-54-0
-56.4
-55-5
-56.0
-57-3
-58.0
-58.6
-57-6
-56.2
-56.2
-55-9
-54-2
-55-4
-55-0
-54-3
-53-5
-53-1
-5i-5
-50.7
-5I-4
-52.0
-52.5
-55-0
-55-7
-54-o
-55-4
-55-7
-57-3
-54-6
-52.4
-54-8
-54-6
-54-o
0.8
0.7
0.2
0.6
0.8
-i-3
2.2
0.7
0-7
0.6
0.0
-0.8
0-3
-0.7
0.4
—0.1
-0.4
-0.5
o-3
f./m.3
7.980
6.661
5-459
5.263
4,739
4.268
3-367
3.424
2.420
2.302
1.662
1.266
0.831
0.694
0.765
0.S76
0-443
0.406
o.37i
0.199
0.178
0.103
0.054
0.031
0.026
0.013
0.013
0.012
0.009
0.009
0.009
0.012
0.012
0.012
o.on
0.007
0.005
0.006
0.005
0.004
0.004
0.003
0.004
0.006
0.006
0.006
0.007
0.006
0.006
0.007
0.008
0.008
0.009
0.010
0.009
0.008
0.008
0.006
0.006
0.007
0.006
0.006
0.004
0.007
0.008
0.006
0.006
0.007
S. 42° E..
S. 43° E..
S. 44° E. .
S. 44° E..
S. 36" E..
S. 280 E..
S. i9°E..
S. 15° E..
S. 4°E..
S. 3°E..
S
S. 3°W.
S. 7°E..
S. 12° E..
S. 8° W.
S. 12° W.
S. 6°W.
S. i'E..
S. 13° E..
S. 6°E.
S. 5°E..
S. 2°E..
S. i'W.
S. 3°W.
M.p.s.
8.2
-7
• 5
.1
■7
• 4
•7 I
•3
:5
.6
.1
• 5 Inversion.
.6
Balloon disappeared
in Ci.
Inversion.
Inversion.
Inversion.
Inversion.
Inversion.
Inversion.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
I29
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued
August 1, 1913 — Continued
Time
Alti-
tude
Pres-
sure
Tem-
pera-
ture
At
Humidity
Rel. Abs.
Wind
Direction Vel
Remarks
p. M
h. n.
12 26.5
12
32.4
12
34-5
12
37-6
12
42.0
12
47-5
12
51-7
12
55-9
I
I
00.4
02.8
M.
16,414
16,000
15,000
14,227
14,000
13,254
13,000
12,441
12,000
11,000
10,857
10,000
9,303
9,000
8,188
8,000
7.058
7,000
6,000
5,719
5. 115
5,000
Mm.
82.0
114. 8
132.9
150.0
190.0
237.2
276.8
322.6
384-0
414.9
°C.
-54-8
-53-8
-5i-4
-49-5
-50-0
-5i-5
-51-3
-50.7
-48.9
-44.9
-44.4
-37-9
-32.7
-30.5
-24-3
-23.5
-19.2
-18.7
-10.2
- 7-7
- 3-6
- 3-0
-0.2
0.1
0.4
0.1
"o'.8
0.5
0.9
g./m.s
0.006
0.007
0.009
0.012
0.011
0.009
0.009
0.013
0.023
0.024
0.052
0.096
0.118
0.196
0.212
0.328
0-343
0.762
0.936
37 1. 4"
M.p.s.
Inversion.
Inversion.
August 2, 1913
A. M.
10 59.0
11 00.3
II 01.5
II
II
II
02.7
04.0
05.0
II
II
06.0
07.0
II
10. 0
II
II
14-5
14.9
II
II
II
19.6
20.0
22.6
II
24.0
II
29.0
II
30-3
II
42-5
II
48.0
II
53-2
12
P
00.0
M.
12
05-5
34
259
437
5oo
584
753
907
1,000
1,059
1 .197
1,500
1,618
2,000
2,289
2,328
2,500
3,000
3,oi5
3,o53
3,307
3,5oo
3,661
4,000
4,437
4,5oo
5 , 000"
5,717
6,000
6,789
7,000
7,912
8,000
9,000
9,086
10,000
io,59i
11,000
12,000
'12,031
13,000
13,168
761.0
741-5
726.5
714-5
701.0
689.0
677-1
666.6
635-3
587-7
584-7
539-0
536.2
520.1
498.3
453-2
247.1
199-3
336.8 , -
161 .1
135-4
25.1
22.8
26.7
27.9
29.0
30.0
29.0
28.5
28.1
27.4
25.4
24.7
21. 1
18.4
19. 1
17-3
12.3
12.2
12.6
10.6
9.9
9.2
6-3
2.9
2.3
0.6
4-6
6.8
12.7
-14.4
-21.7
-22.5
-28.5
-29.0
-37-i
-42.2
-45-6
-54-o
-54-4
-55-2
-55-3
1.0
-2.2
-1.6
-0.6
0.6
0.6
0.5
0.6
1 .0
-1 .1
0.8
0.4
"o'.Z
o.S
0.6
0.9
0.8
'o!8
15.817
14.287
14.788
13-928
12.801
10.212
8.250
7-750
7-312
6.253
5. 828
5.603
5.657
5-454
5.683
5-255
3.986
3.961
4.060
3-197
2.781
2.483
1.840
1.294
1.243
0.922
0.603
0.476
0.272
0-235
0.114
0.105
0.055
0.053
0.021
0.012
13
0.003
12 0.003
13 : 0.003
13 0.003
S. 8^
w..
1.1
S. 64 °
w..
3-3
B.I3-
E...
2.3
S. 62 =
E...
1-5
S.470
W..
3-7
S. 211
E...
3-3
S. 48'
E...
3-1
S. 33 '
E...
4.1
S. 21s
E...
4.9
S. 12°
E...
4.6
S. q =
K...
5-2
S. I"
E...
7.2
S. I1
E...
7-3
S. 7'
E...
18.8
S. 21
E...
7-2
S. 10
E...
7-4
S. 1
E...
7-5
H. 6
K...
9.2
S. n
E...
11. 4
S. 12
E...
11. 2
S. 8
E...
10.4
S. 2
E...
9.0
s
9.0
9.2
S. 7
W..
S.- 5
W..
9.6
S. 4
K...
11. 6
S. 2
E...
11. 5
S. 21- w.
S. 230 W.
S. 260 w.
S. 280 W.
S. 290 W.
S. 300 W.
S. 300 W.
S. 21° W.
S. 20° W.
10.9
10.8
10.7
11. 0
11. 8
11. 8
21.7
23-3
Inversion.
Cloudless.
Inversion.
Inversion.
Inversion.
130
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued
August 2, 1913 — Continued
Time
P. M.
12
Alti-
tude
h. m. M.
11. 0 13,449
12.5 13,815
14,000
14.1 14,284
12 16. 1 14,541
17-3 14,799
15,000
12 22.6
32.0
56.4
15,437
16,000
'16,890
Pres-
sure
Mm.
130.0
122.7
no. 1
105.7
96.0
Tem-
pera-
ture
At
°C.
-54-o
-55-0
-54-i
-52.8
-54-1
-50.3
-50.9
-52.1
Humidity
Rcl. Abs.
Wind
Direction Vel
12 57-9
21,302
21,000
20,000
19,000
18,990
18,000
17,000
16,000
00.0 15,828
15,000
14,000
01.8 13,908
13,000
.... 12,000
03.3' 11,896
35-5
53-9
164.5
-40.0
-42.5
-50.6
-58.8
-58. 7
-61.8
-63.9
-66.6
-67-3
-63-2
-58.5
-58.0
-57-6
-57-3
-57-1
g./m*
0.003
0.003
0.003
0.004
0.003
0.005
0.004
0.004
s.
8' W..
s.
8'W..
s.
8° W..
s.
8° W..
w..
vv..
w..
w..
E...
S. 59° E...
0.012
0.009
0.004
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.002
0.002
0.002
0.002
0.002
Remarks
M.p.s.
19-3
24.3
23.0
20.8
18.3
14.7
18.4
27.2
19.7
7-4
Inversion.
'Inversion. One bal-
loon burst and be-
came detached ; the
remaining balloon
had sufficient lift-
ing force to con-
tinue ascent.
Balloon disappeared.
Few Cu.
Inversion.
""Clock stopped. Altitude computed from ascensional rate.
August 3, 1913
5
07.7
5
5
5
09.4
10.3
11 -3
5
5
13-0
14.0
5
19.9
5
22.8
5
28.0
5
31-0
5
34-o
5
5
37-o
39-0
5
45-8
5
52.0
5
58.0
6
04-8
34 756.9
233
500
54i
754
879
1,000
1,079
1,284
l,5oo
2,000
2,398
2,500
2,838
3,000
3-500
3,804
4,000
4,459
4,500
4,996
5,ooo
5,533
5,792
6,000
7,000
7,183
8,000
8,308
9,000
9.573
10,000
10,790
11,000
739 -S
714-4
697.5
687.7
672.3
656.9
577-7
"s'^'-7
451-3
422.0
394-7
381.8
318.9
273-7
229.7
193.0
26.3
24.1
30.0
30.8
30.3
30.6
30.0
29-5
28.1
26.2
21.8
18.4
17.7
15.8
14.6
10.7
8.4
7-3
4-5
4.2
- 0.2
- 0.5
-3-8
- 6.6
- 8.2
-17.0
-17.4
-24.5
-27.2
-3i. 1
-34-4
-36.8
-41-5
-42.7
-2.2
0.2
-0.2
0-5
0.7
0.9
*o!6'
0.8
I5.I99
13-433
12.014
11.604
7.632
5.585
4-205
3-216
2-979
2.925
2.850
2.649
2.541
2.268
2.109
1.560
1.264
1. 178
0.916
0.9
"o'.fr
'o!6
N.65°W.
N.65°W.
N.620 W.
N.600 W.
S. 8i°W.
S. 75° W.
S. 60 " W.
S. 49° W.
S.46° W.
S. 36° W.
S. 25° W.
S. 9°E..
S. 30° E..
S. 9'E..
S. 39° w.
S.42°W.
S.73°W.
S. 73° W.
S. 79° W.
S. 48° w.
S.44°W.
S.22* W.
S. 18° W.
s
S. 7°E..
S
S. 6°W.
S. 7°W.
S. 8°S..
S. 9°W.
2.7
6.4
5.8
5-4
5-3
5-o
4-5
4.0
4-2
4-9
5-2
6.1
6.6
5.2
2.2
2.3
4-8
4.6
4.2
2.5
2.2
3-5
4.0
5-9
7-6
7-7
7-9
9-4
Few Cu. over mount-
ains on mainland.
Inversion.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
131
Table 4.— Results of sounding balloon ascensions, Avalon, Cal. — Continued
August 3, 1913 — Continued
Alti-
tude
Pres-
sure
Tem-
pera-
ture
At
Humidity Wind
Time
Vel.
Remarks
100 m.
Rel.
Abs. Direction
P. M.
h. m.
M.
12,000
12,050
Mm.
160.6
140.8
132.8
107.0
90.8
88.2
79-4
78.1
76.0
69.4
79-9
88.6
97-8
135-3
166.0
213.6
°C.
—49.2
—49-7
—49.9
-50.1
-Si-3
-54-o
-56.8
—59-2
-65- 7
-65.3
-65.3
-67. 5
-66.9
—62.4
—62.3
-61.8
-61.5
—61.2
-64-3
-65-4
-65-4
—64.0
—57-9
—52.4
—52.2
—50.2
—49.9
-44-5
-37-8
-37-5
P. ct.
g./m3.
S. 14° W..
S. 14° W..
S. 5°W..
S. 7°W..
S. 16° W..
S. 22" W..
S. 290 W..
S.23°W..
S. 4°W..
S. 27° E. . .
S. 260 E...
S. 2°W..
S. 340 E...
S.48°E...
S. 45° E...
S.3i°E...
S. 84° E...
N.32°E...
S. 710 E...
S. 45° E....
S. io° W
M.p.s.
16.4
16.8
22.3
21.3
16.7
18.4
20.3
18.2
12.2
9-4
9.4
9.2
5-3
9.1
9.6
11. 4
17.9
25.8
12.5
7-8
20.3
19. 6
16.5
13-7
0.7
0.0
6 16. 1
6 18. 1
0.4
14,000
14-729
15,000
15,794
15-975
16,000
16,611
16,714
16,895
6 24.0
0.4
6 29.0
6 30.1
0.8
—0.2
Inversion.
6 33-0
6 34.0
6 35-7
0.3
-0.6
-2.5
Inversion.
6 38.4 17,428
0.0
-0.6
16,000
15,838
15,208
15,000
14,000
13, »8
13,000
12,000
1 1 , 782
11,000
6 41.7
6 44.1
0.0
0.6
Inversion.
S. n'W..
S. is° W..
S. i8°W..
6 50.0
0.2
6 54-3
0.7
7 00.3
0.8
7 04.2
8,539 ' 263.6 —25.9
7,080 | 321.0 —16.2
7,000 — i5-7
5,275 405-3 — 5-o
0.7
7 10. 0
0.6
7 17-7
0.6
' 3-i
4,000
3,792
3,5oo
7 24-i
0.8
591-5
6.6
10.6
14-5
17.0
18.9
23-9
26.7
i
1.0
2,000
7 34-i
0.9
1,000
849
718
7 35-9
7 36.7
690.0 1 29.8
0.4
August 7, 1913
P. M.
4 52.0
34
756.4
21.4
78
14.482
E
1.9
Few A. Cu.
few S.
4 55-7
233
739-0
17. 1
2.2
83
11.972
N.si°W..
1. 5
Inversion.
4 57-2
455
720.1
23-2
-2.7
.70
I4-4U
S. 37° w..
2.0
5oo
23-7
66
13-979
S. 53° W..
2.2
4 58.9
665
703-0
26.0
-1-3
49
11. 813
N.6g° W..
3-5
5 00.7
772
694-5
28.8
-2.6
30
8.441
N.8o° W..
6.8
1,000
29.9
21
6.274
N.870 w..
7-i
5 03.0
1,036
674.2
30.0
-0.5
20
6.007
N.88°W..
7.2
5 06.4
i,35o
650.7
30.0
0.0
13
3-905
N.82°W..
7-7
5 07.8
1,440
644.1
28.8
1-3
10
2.814
N.65° W..
4-5
1,500
29-5
9
2.631
N.690 W..
6.4
Inversion.
5 09.4
r,534
637-4
29.8
— 1.1
9
2.674
N.720 W..
7-3
5 12.7
i,74i
622.6
27.0
1.4
6
1.529
N.43°W..
5-i
2,000
26.9
6
1. 521
N.46° W..
6-5
132
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued
August 7, 1913 — Continued
Time
Alti-
tude
P. M.
h. m.
5 i7-o
5
5
23.0
26.0
5
35. 6
5
46.0
5
6
6
58.0
02.0
04-3
6 05.7
6 14.0
6 20
6 24
36
41.0
M.
2,116
2,500
2,S5i
2,796
3,000
3.459
3,5oo
4,000
4,087
4.500
4.708
4,851
4.987
5,000
5,167
5-575
5,88i
5.967
6,000
6,405
6,442
Pres-
sure
Mm.
596-5
567.5
551-5
510. 1
472.3
436
428
421
411
390
374
370
349-1
347-5
Tem-
pera-
ture
1 00 m
°C.
26.8
23.5
22.8
20.5
17.8
11.8
11. 1
0.7
- 0.7
7
9
7
7
-14
-iy
-19
-19
-24
-25
0.9
0-9
Humidity
Rel. Abs.
Wind
Direction Vel
1.6
1-7
0.1
-0.7
0.8
1-4
0.7
0.8
0-5
v./m'6
1. 512
1.256
1.207
1-234
1-353
1.253
1.300
1.065
1.007
1.299
1.292
1.056
1.338
1.362
1-432
0.979
0-594
0.450
0.432
0.221
0.169
N.48'
N. 7'
N.14'
N. 8'
N. 7'
N.40'
N.40
N.34'
N.33
W.
E..
E..
W.
E..
E..
E..
E..
E..
N.32°
N.320
M.p.s.
7-i
4-7
4.2
3-i
3-5
4-5
4.6
6.4
6-7
7-8
8-4
Remarks
5/10 A. Cu.; S.
At the base of A. Cu.
5:57 p. m. Balloons
disappeared.
Inversion.
August 8, 1913
5 23.5
5 25.1
5 26.
5 27.4
5 28. 41
5 29.1
5 29.51
5
5
30.2
30.7
5
32.3
5
34-3
5
36.9
5
40.5
5
43-4
5
5
46.8
47.1
5 48.0,
5 49-2
50.8
53-2
34 755-6
367 726.6
500
691.5
1,000
1,021
1,122
1,244
1,413
1,500
1,539
1,711
2,000
2,080
2,500
2,619
3,000
3,3i6
3,500
4,000
4,198
4,5oo
4.981
5,000
5,982
5,997
6,000
6,299
6,615
6,840
7,000
7,o5o
7,750
8,000
672.6
664.7
655.4
642.9
633-6
621.3
595-4
[ 559-2
J 514-7
I 462.6
419.9
369-6
368.4
354-5 —
20.0
17.2
16.4
14.4
19.8
20.4
21.8
24-5
24-9
24.4
24.2
24-3
23.1
22.6
19-3
18.4
14-5
11. 4
9.8
5-8
4.2
2.2
- 0.9
- 1.0
- 6.5
- 6.9
- 6.8
8-7
-8.9
- 9.1
-13-0
-14-5
75
0.8 80
.... 82
0.7 J 88
.... 67
2.6 64
1-4 I 56
2.2 49
0.2 j 45
— ! 43
0.6 j 42
0.1 41
.... 39
0.5 I 39
— : 40
0.8 40
— j 41
1.0 41
•••■ 43
.... 46
0.8 I 48
.... 50
0.7 53
53
0.6 \ 57
2.7 i 59
.... 58
0.6 58
0.1 ! 54
0-5
0.6
11.608
11.342
10.785
11.336
11. 213
10.640
10.859
10.200
9.476
9-I5I
8.984
7.983
7-758
6.572
6.233
5-055
4.176
3.961
3.278
3-079
2.806
2.387
2.368
1.634
1-637
1.623
1.390
1.326
1.308
1. 180
1 -137
0.763
0.655
S. 320 W.
S. 32^ w.
S.62°W.
N.55° W.
N. 6°E..
N.i2°E..
N.i6°E..
S. 69° E..
S. 77° W.
N.82° W.
N.730 w.
N.450 w.
N.210 w.
N.i5° W.
N.250 W.
N.28° W.
N.200 W.
N.i3°W.
N.io'W.
N. 2°W.
N. i° E..
N.i7°W.
N.45°W.
N.450 W.
S. 50° w.
S. 53° W.
S. 53° W.
S."750 W.
S. 45° W.
S. 22° W.
S.u'W.
S. 7°W.
S. 14° w.
S. 16° w.
4-3
4-3
3-3
0.9
I.Q
2.0
0.4
0.2
1.0
1-5
1.8
5.2
6.0
6.2
3-6
2.8
4-1
5-2
4.6
3-2
2.7
3-0
3-4
3-4
3-o
5.8
3-0
5-5
3-6
14.6
12.0
10.7
11. 5
12.8
4/10 S. Cu. SSE.
Balloons in S. Cu.
NW. Inversion.
Inversion.
Inversion.
Pressure pen not re-
cording. Altitude
computed from as-
censional rate.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
133
Table 4. — Results of sounding balloon ascensions, Avalon, Cal. — Continued
August 8, 1913 — Continued
Time
Alti-
Pres-
sure
Tem-
pera-
ture
At
Humidity
Wind
Rel.
Abs.
Direction
Vel.
tude
100 m.
Remarks
P. M
h. n
5 54-8
5 56.2
5 56.8
s
s
57-7
59-8
6
6
02.2
03.1
6
05.8
6
6
07. 5
09.4
6
11. 2
6 13. i
M.
8,21s
8,650
8,850
9,000
9,080
9,700
10,000
10,41s
10,730
11,000
",S75
12,000
12,080
12,700
13,000
13,250
14,000
14,100
Mm. °C.
! -iS. 9
; -19-5
! — 20.7
! —21.3
-21.7
i —24-3
—26.1
-28.7
' —29.8
-31-5
! — 35-o
! -35.8
; —36.0
—37-2
! -38.7
j -39-8
: —43-4
; —43-9
0.6
0.8
0.6
0.4
0.4
0.6
0-3
0.2
0.2
0.5
0.5
P. Ct.
45
45
45
44
44
43
43
42
42
42
42
41
41
40
40
40
40
40
0.582
0.422
0-375
0.346
0-334
0.256
0.215
0.162
0.14S
0.124
0.086
0.077
0.076
0.065
0.055
0.049
0.033
0.031
S. 180 W..
M.p.s.
14.0
6/10 S. Cu. SSE. Bal-
loonsdisappeared in
St. Cu. Observa-
tions of ascension
were made through
this film of St. Cu.
which at times ob-
scured balloons
after 5:26.5 P. m.
August 10, 1913
4 43-o
4 45-7
4 4
4 49-2
4 S2.4
4 54-9
00.9
03.0
09.0
11. o
S I3-I
16.6
18.3
34
435
5oo
832
1,000
1,036
1,500
1,549
1,976
2,000
i,5oo
1,385
1,253
1,000
785
702
600
500
360
263
765.9
722.6
690.3
674-3
635.7
604.8
647.8
657-7
694.2
700.8
728.9
737-1
23.4
21.3
21.9
24.7
24-5
24-5
23.3
23.2
19.3
19.0
21.0
21.5
22.4
24-5
26.2
24.1
24-3
23-7
23.0
21.3
0.3
0.6
0.7
0.8
-0.3
0.2
12.077
10.522
9-937
6.052
4-654
4-432
3.106
2.882
2.464
2.421
2.358
2.428
1.770
1-773
1,706
I-5I7
1-534
3-389
5-495
8.122
N.46°E..
N.24°E..
N. 5°E..
N.89°W.
S. 88° W.
S.87°W.
N.47" w.
N.42°W.
N.470 W.
N.470 W.
N.43°W
N.420 W.
N.230 W.
N.44°W.
N.610 W.
N.68°W.
1.1
1-7
4.0
3-5
3-4
2-3
2.1
1.5
3-9
Cloudless.
Inversion.
One balloon became
detached; the other
balloon with the
meteorograph slow-
ly descended.
Inversion. Balloon
disappeared behind
the mountains.
The distribution of pressure at the earth's surface changes but little in
type, and that never abruptly, during the period of observation, nor does the
pressure itself vary much from day to day. Figures 7 and 8 show the pressure
distribution in a general way for the whole period. The positions of the
centers of high and low pressure at 8 a. m. or 8 p. m., seventy-fifth meridian
time, are shown by the circles, in which dates are also indicated. In the case
of high pressure, these circles are connected by solid lines ; in the case of low
pressure, by dashed lines.
In three of the ascensions, July 24 and 27 and August 3, the balloons were
followed with the theodolite beyond the altitude at which the minimum tern-
134 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
perature was recorded (see fig. 9). In another, August 2, the air movement
could be observed up to 17 kilometers. On July 24 and 27 the winds were
westerly, with a small south component up to the height at which the minimum
temperature was found. Above this height the wind was easterly. On
August 2 and 3 the winds were southerly, with a small west component up to
the point of minimum temperature. Here again the winds became easterly.
On July 24 the wind velocity increased as the easterly component made its
appearance ; on July 27 there was little change ; on August 2 and 3 there
was a decided decrease in velocity as the wind became easterly.
B. The Captive Balloon and Mountain Observations on and Near
Mount Whitney
By W. R. Gregg
Meteorological observations, including some captive balloon ascensions,
were made at Mount Whitney, Cal., from August 1 to 13, inclusive, and at
Lone Pine, Cal., from August 1 to 4, inclusive. Mount Whitney is the highest
peak of the Sierra Nevadas, its altitude being 4,420 meters. It lies in latitude
36° 35' N. and longitude 118° 17' W. On the north, south, and west it is
surrounded by mountains, many of which are nearly as high as itself; its
eastern slope is quite precipitous and at its foot lies Owens Valley, which is
about 25 kilometers in width and extends in a north-northwest and south-
southeast direction. East of this valley and running parallel to the Sierras
is the Inyo Range, altitude about 3,000 meters. Lone Pine is situated about
midway between these two ranges, near the northern end of Owens Lake.
Its altitude is 1,137 meters and it lies in latitude 360 35' N. and longitude 1180
3' W., about 25 kilometers due east from Mount Whitney. Topographically
the location of Lone Pine is similar to that of Independence, Cal., which is
about 25 kilometers north-northwest of it and therefore practically the same
distance from Mount Whitney. Independence is in latitude 360 48' N., longi-
tude 1180 12' W., and has an altitude of 1,191 meters, or 54 meters higher
than that of Lone Pine.
SURFACE OBSERVATIONS AT MOUNT WHITNEY
The instrumental equipment consisted of a Short and Mason aneroid
barometer, sling psychrometer, small kite anemometer of the Robinson type,
Marvin meteorograph, and Richard meteorograph. The Richard instrument
recorded pressure and temperature only and the object in taking it was to
obtain a surface record of these elements and also to provide a substitute in
case the Marvin instrument were lost or injured. The latter recorded relative
humidity in addition to pressure and temperature. In order to secure good
ventilation during balloon ascensions a section of the horizontal screening
tube containing the humidity and temperature elements had been cut out, thus
exposing these elements directly to the air.
As soon as they were unpacked, both of these instruments were started
recording and a continuous record of pressure, temperature, and relative
humidity was obtained. The sheets were changed at 8 a. m. and 5 p. m., and
eye readings of the aneroid barometer and psychrometer were taken at these
times; also at 11 a. m. and 2 p. m., and during balloon ascensions. In addi-
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 1 35
tion, readings of the psychrometer were taken by (Messrs. A. K. Angstrom
and E. H. Kennard, representing the Smithsonian Institution, during the
nights when they were observing. These readings have also been used to
check the meteorograph records.
The exposure of the instruments was fairly good. They were kept in an
improvised shelter constructed from the boxes in which they were " packed "
to the summit. The ventilation was good, but during those afternoons in
which the sun shone, the air in the shelter was considerably heated. How-
ever, there were only four sunny afternoons, and furthermore, the eye readings
at 2 p. m. and 5 p. m. leave but little interpolation necessary.
All of the instruments were calibrated before and after the expedition.
Especial care was taken in the calibration of the aneroid barometer, tests being
made to determine the correction for "lag" or "creeping" and for changes
in temperature. The effect of the latter was found to be negligible.
Owing to the large scale value of the pressure elements in the meteorographs
and to the effect of changes of temperature on those elements, it is impossible
to obtain with much accuracy the hourly values. However, in table 5 are
given the pressures observed at certain hours. The readings at 11 a. m. are
uniformly higher than those at S a. m., 2 p. m., or 5 p. m. It is probable that
the diurnal maximum occurs at about this time.
The range of pressure for the entire period is large, about 8 mm. The
range for the same period at Independence is much less, about 5 mm. At
both places the lowest readings were recorded on August 8 and 9, while a
cyclonic disturbance was central over northern California. This low was
attended by considerable cloudiness, with thunderstorms, and, at Mount
Whitney, snowstorms. The greater pressure range at Mount Whitney than
at Independence is accounted for by the cool weather during the passage of
the low and the consequent crowding together of the isobars in the lower
levels.
Tables 6, 7, and 8 contain the hourly values of temperature, relative humidity,
and absolute humidity, respectively. Means have been computed for the 10
complete days, August 3 to 12, inclusive. Final conclusions may not be drawn
from so short a record, but a few comparisons are of interest. The mean
temperature was 0.7° C. ; that in the free air at the same altitude and for the
same time of year, as determined from five years' observations at Mount
Weather, Va., is — 2.00. The mean temperature at Pikes Peak1 for these
10 days in 1893 and 1894 was 2.8°. Pikes Peak has an altitude of 4,301 meters,
or about 100 meters below that of Mount Whitney, and to correct for this
difference in altitude about 0.6° should be subtracted from the value at Pikes
Peak. The temperature at Mount Whitney was undoubtedly below normal,
owing to the severe stormy weather which prevailed. However, the values at
both places, compared with those at the same altitude above Mount Weather,
indicate that in summer temperatures on mountains are higher than those in
the free air, although difference in latitude, in this case about 2^°, should
be considered. The times of maximum and minimum temperatures at Mount
Whitney were 3 p. m. and 5 a. m., respectively; at Pikes Peak they were
1 p. m. and 5 a. m., respectively.
1 Annual Reports of Chief U. S. Weather Bureau, 1893, 1894, 1895-1896,
Washington.
136
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
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NO.
RADIATION OF THE ATMOSPHERE ANGSTROM
137
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138
SMITHSONIAN MISCELLANEOUS COLLECTIONS
VOL.
65
Figure 10 shows mean hourly temperatures at Mount Whitney and Inde-
pendence and for the same period during 1893 and 1894 at Pikes Peak. The
range at the latter appears to be somewhat smaller than at Mount Whitney,
and this may be due to the fact that conditions at Pikes Peak are more nearly
like those of the free air, owing to its isolation and the consequent freer
circulation. The curve for Independence shows the large diurnal range
characteristic of valley stations. Beneath the mean temperatures for Mount
Whitney in table 6 are given the means for the same period at Independence
and the differences in temperature change per 100 meters altitude between
Tem.12 1 2 3 4 5 6 7 8 9 10 11 12- I 2 3 4 5 6 7 8 9 10 11 12Tem.
C
5
4
3
2
1
0
-1
31
30
29
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25
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S3
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20
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AIM.
PM.
5
4
3
2
1
0
-1
31
30
29
28
27
86
25
24
23
22
21
20
19
18
17
16
|
i
Y
P/KE'5 PEAK, /tOL.
v~~\- | | 1 \^\
/■ '
MT. WP/TA/EY, CAL^
1 1
/
/
! 1
i
/
\
A
1
i
I
/PDEPENOENEE, /CAIL.
1
\
S
\^
10
Fig. io. — Mean hourly temperatures at Mount Whitney and Independence,
Cal., August 3 to 12, inch, 1913, and at Pikes Peak, Col., August 3 to 12, inch,
1893 and 1894.
the two places. The temperature change with altitude during the night hours
is somewhat misleading, owing to a marked inversion of temperature between
the surface of the valley and about 200 meters above it, as will be pointed out
in discussing the Lone Pine observations. The hourly differences between
Independence and Mount Whitney during the daytime are large, averaging
about 0.85. The mean for the 24 hours is 0.73.
The relative humidity, table 7, was probably higher than normal for this
season of the year, owing to the unusually stormy weather and the presence of
snow on the ground. The mean was 69 per cent, the mean maximum 79 per
cent at 7 to 8 p. m., and the mean minimum 61 per cent at 4 a. m. During the
severe storm of August 8, 9, and 10, 100 per cent was frequently recorded.
The absolute minimum was 15 per cent at midnight of the 12th.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
139
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140 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
For the reasons given above, the absolute humidity, table 8, was also probably
higher than normal. The mean was 3.5 grams per cubic meter, the mean
maximum 4.2 at 4 to 5 p. m., and the mean minimum 2.7 at 4 a. m. The abso-
lute maximum was 6.2 at 7 p. m. of the 7th and the absolute minimum 0.6 at
midnight of the 12th.
Table 9 gives roughly the average wind velocities. Dial readings of the
anemometer were made at the times indicated by stars. The figures between
these stars represent average velocities for the intervals between readings.
The mean for the entire period was 3.0 m. p. s. That at Pikes Peak for the
same time of year was 6.0 m. p. s. This difference may be due partly to the
fact that Pikes Peak stands out in the open, whereas Mount Whitney is
surrounded by peaks nearly as high as itself, and also to the greater proximity
of Pikes Peak to the cyclonic storm paths of the United States. The prevail-
ing wind direction was southeast, but directions ranging between south and
northeast were frequently observed, and a southwesterly wind prevailed during
the blizzard of August 9.
In table 10 may be found the state of the weather for the period, together
with notes on storms, kinds of clouds, and miscellaneous phenomena.
FREE-AIR OBSERVATIONS AT MOUNT WHITNEY, CAL.
The place from which balloon ascensions were made was about 60 meters
to the northwest of the summit of Mount Whitney and about 10 meters below
it. This was the only spot on the mountain that was fairly level and free
from jagged surface rocks. While the balloon was being filled with gas it
rested on a large piece of canvas to protect it from rocks and snow. The
gas, compressed in steel cylinders, was furnished by the Signal Corps of the
United States Army. A hand reel was used for reeling the wire in and out.
Readings of the psychrometer, aneroid barometer, and anemometer were made
with the aid of a pocket electric flash lamp.
Ascensions were made on only three nights, August 3, 4, and 5, and were
begun immediately after sundown. On all other nights the weather was either
too windy or too stormy. The balloon was allowed to take as great an altitude
as possible and was then kept out until the wind aloft had increased to such
an extent that it was necessary to reel in.
Table 11 contains the tabulated data for the three records obtained, and in
figures 11 and 12 are plotted the temperature and absolute humidity gradients,
respectively ; the slight changes with time at the higher levels in each ascension
are not plotted ; only the ascent and descent proper. On August 3 and 4 these
elements diminished with time by nearly the same amounts at all upper levels
as at the surface. There was but little wind during these nights. On August
5, however, there was a fairly high northeast wind aloft and the temperature
and humidity changed very little with time. The change with altitude in
temperature was greater and in absolute humidity less than on the other
nights.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
141
Table ii. — Results of captive balloon ascensions at Mount Whitney, Cal.,
August 3-5, 1913
Date and hour
Surface
At different heights above sea
Pres-
sure
Tem-
Bel.
pera-
ture
hum.
°C.
P. ct.
0.6
80
0.3
81
O.I
80
0.3
78
0.2
78
0.3
75
0.3
73
0.3
74
0.2
75
0.2
76
O.I
78
0.0
79
— 0.2
85
2-3
77
2.2
7«
2.0
76
1.8
74
1.6
72
1.6
7i
1.6
70
i-3
67
1.1
60
1. 1
55
1.1
5o
0.9
46
0.8
45
0.6
51
0.6
5i
0.6
51
2.8
51
2.5
52
1.8
50
1.8
45
1.9
47
1.8
53
i.7
57
i-3
55
1.2
55
1-3
55
1-3
5i
1.2
46
1.1
38
Wind
direc-
tion
Height
Pres-
sure
M.
Mm.
4,410
446.2
4.533
439-3
4.631
434-0
4,689
430.9
4,801
424.9
4.683
431.2
4,801
424.9
4.744
427.9
4,802
424.9
4,664
432.4
4,579
437-0
4,509
440.9
4,410
446.5
4,410
446.1
4,627
434-3
4,852
422.3
5,104
409.1
5,359
396.1
5,230
402.6
5,3i6
398.3
5,2i6
403-3
5,258
401.2
5,201
404.0
5,229
402.6
5.299
399-0
5,198
404.0
4.634
433-6
4,509
440-5
4.410
446.0
4,410
446.0
4.625
434-3
4,810
424.4
4,995
414.7
4.997
414.7
4,898
419.9
4.999
414.7
4,861
422.1
4,736
428.9
4,820
424.4
4,734
428. Q
4.604
435-8
4,410
446.1
Tem-
pera-
ture
Humidity
Rel.
Abs.
Wind
dir.
Aug. 3, 1913:
7:13 p. m...
7:18 p. m...
7:25 p. m...
7:35 p. m...
7:45 p. m...
7:58 p. m...
8:06 p. m. . .
8:10 p. m. . .
8:15 p. m...
8:18 p. m...
8;3i P. m...
8:41 p. m...
8:51 P. m...
Aug. 4, 1913;
6:45 p. m...
6:49 p. m...
6:56 p. m...
7:04 p. m. . .
7:12 p. m. . .
7:22 p. m.. .
7:45 p. m...
7:56 p. m...
8:25 p. m..'.
8:55 P- m...
9:13 p. m...
9:39 p. m...
10:00 p. m..
11:45 P- m..
11:50 p. m..
12:00 mdt..
Aug. 5, 1913:
6:38 p. m...
6:54 P- m...
7:30 p. m. . .
7:37 P- m...
7:52 p. m...
8:05 p. m...
8:17 p. m...
8:42 p. m. ..
8:56 p. m...
9:05 p. m. ..
9:20 p. m.. .
9:44 P- m...
11:00 p.m..
Mm.
446.2
446.2
446.2
446.3
446.3
446.3
446.3
446.3
446.4
446.4
446.4
446.4
446-5
446.1
446.2
446.2
446.2
446.2
446.2
446.3
446.3
446.3
446.2
446.2
446.2
446.2
446.0
446.0
446.0
446.0
446.1
446.2
446.3
446.4
446.4
446.5
446.6
446.7
446.7
446.6
446-5
446.1
S.
s.
s.
Calm.
Calm.
E.
E.
E.
E.
E.
ENE.
ENE.
ENE.
Calm.
Calm.
Calm.
Calm.
Calm.
Calm.
Calm.
Calm.
E.
Calm.
Calm.
Calm.
Calm.
E.
E.
E.
Calm.
Calm.
Calm.
Calm.
Calm.
Calm.
Calm.
Calm.
Calm.
NE.
NE.
NE.
NE.
°C.
0.6
-0.2
-0.9
-1.5
-2.3
-0.8
-1-5
-1-3
-2.3
-2.0
-1-5
-0.7
-0.2
2.3
1.4
-0.9
-2.2
-4.8
-4.4
-5-6
-4.9
-4.4
-3-6
-3-6
-5-6
-4-3
-1.9
-0-7
0.6
2.8
0.8
-1.4
-2.8
-3-5
-2.7
-3-4
-0.3
1.0
1.1
P. ct.
./cu.m.
4.0
3-i
2.9
0.8
0.7
0-5
3-1
4.0
2.9
i-5
1.1
1.1
0.7
0.8
0.6
0.4
0.4
0.4
0.4
0.4
1.1
2.6
3-o
2.8
2.3
2.1
2.0
2.1
2.0
2.3
2.5
2.4
2.4
2.5
2.0
S.
ESE.
ESE.
E.
E.
E.
E.
E.
E.
E.
ENE.
ENE.
ENE.
Calm.
Calm.
Calm.
Calm.
SSW.
S.
WSW.
WSW.
SW.
SSW.
SSW.
S.
s.
E.
E.
E.
Calm.
SW.
NE.
NE.
NE.
NE.
NE.
NE.
NE.
NE.
NE.
NE.
Njs.
Aug. 3, 1913. — One captive balloon was used; capacity, 28.6 cu. m.
Few Cu., from the east, prevailed throughout the ascension.
Aug. 4, 1913. — One captive balloon was used; capacity, 28.6 cu. m. ; lifting force at
beginning of ascension, 5.4 kg.
Few Cu., from the south, at 7 p. m. Cloudless by 9 p. m. Lightning was seen over or
near Death Valley. There was considerable electricity on the wire.
Aug. 5, 1913.^ — One captive balloon was used; capacity, 28.6 cu. m.
Few Cu., direction unknown, in early evening. Cloudless after 8.50 p. m. Lightning
was seen on the eastern horizon, near Death Valley.
142
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Alt.
km
53
5.2
6.1
50
4,9
48
4.7
46
45
44
AUB j
AUG . 4
AUG 5
Alt
km
53
52
5,1
50
49
48
4.7
46
45
44
A5CCNT O—O-O
DESCENT *■
\
\
V
\K
V
V
V,
Ir
a
Tem°C
-2°-l° 0°
-5"-<
-3u-2u-r 0° 1" 2" 3'JTem.°C
Fig. 11.— Temperature gradients (°C), above Mount Whitney, Cal., August
3, 4, and 5, 1913.
Alt.
km
5.4
5.3
5.2
5.1
5.0
4.9
4.8
4.7
4.6
4.5
Abs. Hum,
g./cu.m.
AUG. 3.
AUG. 4.
A UG. S.
Alt.
|
km
5.4
5.3
5.2
5.1
50
4.9
4.8
4.7
4.6
4.5
hh Hum,
g./M,
J ASCENT. O—O—O
~| DESCENT, x x x
n
^
v
\
k
k
\
\
\
\
\
K
\
IZ
\
&
N
N<
\
/ 1
0 12 3 4
0 12 3 4
2 3 4
.fig. 12. — Absolute humidity gradients, grams per cubic meter, above Mount
Whitney, Cal., August 3, 4, and 5, 1913.
Table 12. — Temperature differences at 100-meter intervals above Mount
Whitney, Cal., August 3, 4, 5, 1013
Altitudes (meters)
Observations
I 100
200
300
400
500
600
700
800
900
Aug. 3, 1913:
Aug. 4, 1913:
Aug. s, 1913:
0.6
. 0.5
.: 0.4
i-3
. 0.9
O.I
0.63
0.8
1.0
0.4
1.0
1.0
O.I
0.72
0.9
0.4
0.9
0.5
I.I
0.9"
0.77
0.6
0.2
1.0
0.4
1.2
1.2
O.77
0.7
0.5
o.S
1.1
0.78
o.S
0.4
0.8
1.2
0.72
0.6
0.4
1.0
0.4
1.0
0.4
0.50
0.70
0.70
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
143
Table 12 contains the temperature differences at 100-meter intervals above
the surface, as observed in all three ascensions. The mean gradient is 0.70
and is fairly constant at all altitudes up to 900 meters.
FREE-AIR OBSERVATIONS AT LONE PINE, CAL.
The balloon ascensions were carried out by Mr. P. R. Hathaway from a
place about 1 kilometer north of Lone Pine. The Instrumental and other
equipment was similar to that used at Mount Whitney. Owing to leakage of
a large number of gas tubes, only four ascensions were possible. These were
made on August 1, 2, 3, and 4, and were begun shortly after sundown. Surface
conditions for making ascensions at this time of day were usually excellent.
Table 13. — Results of captive balloon observations at Lone Pine, Cal.,
August 1-4, 1913
Surface
At different heights above sea
Date and hour
Pres-
sure
Tem-
Rel.
pera-
ture
hum.
°C.
P. ct.
16.7
79
16.7
79
16.8
78
17.2
77
18.3
72
16.7
80
16.7
78
16.7
7«
23-9
46
24.2
45
22.6
48
19.4
64
19.7
57
18.6
66
17.5
6q
18.0
64
16.4
77
16.7
75
17.0
70
17.2
70
21 .7
54
21.7
54
22.9
37
19.9
58
19.8
57
21 .0
43
22.2
39
22.7
38
23.O
38
26.4
27
Wind
direc- jiHeight
tion
Pres-
sure
Tem-
pera-
ture
Humidity
Rel.
Abs.
Wind
dir.
Aug. 1. 1913:
9:18 p. m
9:30 p. m
9:37 P- m
9:44 p. m
10:10 p. m
10:15 p. rrr. ..
10:43 p. m. . . .
10:48 p. m
Aug. 2, 1913: '
7:38 p. m
7:41 P- m
7:47 P- m
8:01 p. m..
Mm
660
660
660
660
660
660
661
661
658
658
659
8:48 p. m 660
660
662
662
662
662
662
662
661
661
664
656
657
657
658
65S
658
658
9:30 p. m. . .
10:48 p. m. .
10:56 p. m. .
11 :o5 p. m..
11:13 p. m..
11 :i9 p. m. .
11 :25 p. m. .
Aug. 3, 1913:
7:17 p. m.. .
7:21 p. m. . .
9:25 p. m. . .
Aug. 4, 1913:
7:19 p. m...
7:22 p. m...
7:34 P- m...
7:56 p. m...
8:02 p. m. . .
8:05 p. m...
8:55 P- m...
Calm.
Calm.
Calm.
Calm.
W.
Calm.
S.
S.
NNW.
NNW.
NNW.
S.
Calm.
Calm.
S.
S.
S.
S.
w.
w.
Calm.
Calm.
SSW.
Calm.
Calm.
Calm.
S.
S.
S.'
s.
M.
1,137
1,190
1,296
1,297
1,311
1,47°
1,204
1,137
i,i37
1,253
1,355
1,958
2,273
1,811
1,724
1,728
1,432
1,316
1,234
i,i37
1,137
1,296
I.I37
I,i37
1,309
2,367
2,106
1,629
i,459
i,i37
Mn
660
656
647
636
655
661
658
649
642
600
579
612
618
619
641
649
655
662
650
664
656
644
572
589
622
634
658
°C.
16.7
21 .1
22.2
21.4
23-0
23.1
22.3
16.7
23-9
27.2
27.1
23.0
19.2
22.7
22.9
21.9
24-3
25.6
25-5
17.2
21.7
28.4
22.9
19.9
20.6
23.2
24.4
28.9
30.6
26.4
P. ct.
79
50
37
37
28
24
46
78
46
30
17
17
23
./cu.m.
11. 1
9.1
7.2
6.9
5-7
4.9
9.0
11. 0
0-9
7-7
4-4
3-5
3-8
4.0
4.0
4.0
5-0
5-0
4.9
10.2
10.2
7.2
7-5
6.7
Calm.
W.
W.
W.
W.
W.
S.
S.
NNW.
N.
N.
Calm.
SE.
SE.
SW.
SW.
SE.
E.
E.
W.
Calm.
SSE.
SSW.
Calm.
SE.
SE.
SSE.
SSE.
SSE.
S.
Aug. i, 1913.- — One captive balloon was used; capacity, 28.6 cu. m. Cu. Nb., from the
west, decreased from 5/10 to a few. Light rain fell for about two minutes at 9.35 p. m.
Aug. 2, 1913. — One captive balloon was used; capacity, 31. 1 cu. m. St. Cu., from the
south, decreased from 6/10 to a few.
Aug. 3, 1913. — One captive balloon was used; capacity, 31. 1 cu. m. 1/10 Cu., direction
unknown, disappeared before the end of the ascension.
Aug. 4, 1913. — One captive balloon was used; capacity, 31.1 cu. m. The sky was
cloudless.
si
-J
o
00
0
SB
en
i/1
CM
0
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°«X>
04
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00
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CO
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CO
D
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co
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SSI
T
CO
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6
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co
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cvt
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CO
cm
°o
©J
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co
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9 ^
V :
O 5
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1
w
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HC0C<li-lO0S00r-cDlO'O<C0<M'-
,y «i W N N i- i .-i — i ,-t _ ,-< r-i i-i r
O
u
CU
H-l
u
H
NO.
RADIATION OF THE ATMOSPHERE — -ANGSTROM
145
The records obtained in the balloon ascensions are given in tabular form in
table 13. Figures 13 and 14 show the temperature and absolute humidity
gradients, respectively. There was always a marked inversion of tempera-
ture between the surface and 200 meters above it, amounting on the average
to 6° C. (See table 14.) From 200 to 300 meters there was practically no
change, but above 300 meters the temperature decreased with altitude at a
Alt.
AUG. 1
aue e.
AUG. 3.
Alt.
km
2.2
21
2.0
19
18
17
1.6
1.5
1.4
13
1,2
Abs. Hum.
x
km
2.2
2.1
2.0
1.9
18
1.7
1.6
1.5
14
1.3
12
1
ASCCNT. O—O—O
j
DC5CENT.
\\
V
\
\
\\
C
^
\>
V,
"x
S
<s
^
<-
^
K
m
r
^
0
m
>
5 8 7 8 0 10 11
3456789 10
7 D 9 19
to, Hum,:
r./cu.m,
Fig. 14.-
-Absolute humidity gradients, grams per cubic meter, above Lone Pine,
Cal., August 1, 2, and 3, 1914.
Table 14. — Temperature differences at 100-meter intervals above Lone Pine,
Cal., August 1-4, 1913
Altitude (meters)
Observations
100
200
300 1 400
Soo
600
700
800 900
1,000
1,100
1,200
Aug. 1, 1913:
-4.8
-5-7
-2.7
-8.3
-4.2
-6.2
-i-3
-4-74
-1-5
-0.3
-0.5
O.I
—0.1
-0.3
0.5
1 .1
Aug. 2, 1913:
Aug. 3, 1913:
0.7
0.8
0.7
0.8
0.7
—0.2
0.7
0.4
0.6 1.1
0.7 0.8
1.2
0.7
1 .2
0.8
Aug. 4, 1913:
-4-3
—1-3
—1.30
0.7
—1-3
O.IO
0.7
o.S
0.68
0.7
1.0
0.S0
0.7
0.9
0.52
0.6
1 .0
0.68
0.7
0.9
0.72
•
0.7
O.Q
0.88
0.7
0.8
0.85
0.7
0.5
0.80
0.7
0.5
0.60
fairly uniform rate, the mean difference per 100 meters being 0.73. On
August 2 there was about equal cooling with time at all levels ; on the 4th
the temperature changed but little at upper levels and increased somewhat at
the surface.
The absolute humidity (fig. 14) diminished rapidly from the surface to the
altitude at which the highest temperature was recorded. Above this, on
August 2, the only night in which a record of humidity at higher levels was
obtained, it diminished slowly.
146
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
"9
fcfl
^,
V.
C]
<
hfl
cfl
oO
U
C
Ih
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no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
147
During the day there was a moderate breeze from the north blowing down
the valley. This became very light toward evening, and at about the same
time the temperature began to fluctuate, sudden changes of 2° to 50 C.
occurring frequently between 6 p. m. and the time of minimum temperature.
These fluctuations are well shown in the thermograph records at Inde-
pendence, Cal. (fig. 15), and in table 15, which contains observed temperatures
and humidities at Lone Pine, Cal. These observations have been referred to
by Dr. Wm. R. Blair in his discussion of mountain and valley temperatures
(Bulletin Mount Weather Observatory, Washington, 1914, 6:122) and are
in accord with the conclusion there reached that " there is not a stream of
cool air past the slope station, but a direct convective interchange between
Table 15. — Fluctuations in surface temperature and humidity at Lone Pine,
Cal., August 2 and 3, 1913
Date
Time
Tem-
Relative
Absolute
perature
humidity
humidity
1913
P. m.
•c.
Per cent.
g./cu. m.
7:43
7:51
22.2
48
56
9-3
9.9
20.6
8:01
19.4
64
10.6
8-45
20.0
56
9.6
9:10
16.7
75
10.6
9:21
18.7
64
10.2
10:01
16.7
75
10.6
11 :oo
18.3
62
9.6
11:05
16.4
77
jo. 7
11:48
18.9
60
9.6
6:50
7:40
25.1
40
56
9.2
10.2
21. 1
7:So
I9.4
56
9-3
8:05
20.8
45
8.1
8:37
19.4
52
8.6
9:09
21. 1
42
7-7
9:33
23-9
34
7-3
9:43
21.8
47
8.9
the cool air on the slope and the free air over the valley at the same or
slightly lower levels." In general, as shown in table 15, the lower tempera-
tures were accompanied by the higher absolute humidities.
Between 8 and 10.30 p. m. it was necessary to bring the balloon down
because of southerly or southeasterly winds aloft. These winds gradually
extended toward the surface and were warm and dry (table 13). The mixing
of the upper southerly and the lower northerly currents seems to account for
the variations in surface temperature and humidity already referred to.
The fact that the upper southerly wind is warm and dry suggests the
probability that it originates over the Mohave Desert, which is about 150 kilo-
meters south of Lone Pine. The heating and consequent rising of air over
the desert in the daytime, which gives rise to the southerly current aloft, at
the same time causes the surface northerly current down the valley.
APPENDIX II
SUMMARY OF SPECTROBOLOMETRIC WORK ON MOUNT WIL-
SON DURING MR. ANGSTROM'S INVESTIGATIONS
By C. G. Aebot
Table 16, similar in form to tables 35 and 36 of Vol. Ill of the
Annals of the Astrophysical Observatory of the Smithsonian Institution,
contains a summary of all Mount Wilson spectrobolometric observations
obtained by Mr. Aldrich, with accompanying measurements and reductions,
for days in which Mr. Angstrom obtained observations in California in 1913.
The final column is of interest in connection with the pyrheliometric observa-
tions on Mount Whitney, given in Appendix III. The third column contains
spectroscopic determinations by Mr. Fowle of the total depth of precipitable
water existing as vapor above the observing station at Mount Wilson (latitude
340 12' 55" N., longitude 1180 03' 34" W., elevation 1,727 meters or 5,665 feet).
The letters given under " grade " have the following meanings : vp, very
poor; p, poor; g, good; vg, very good; e, excellent. All observations were
made between 6 and 10 o'clock in the morning except those of August 8,
which were made between 2 and 6 o'clock in the afternoon. For a discussion
of the methods and apparatus used the reader is referred to Vol. Ill of the
Annals, cited above.
148
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
149
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APPENDIX III1
SOME PYRHELIOMETRIC OBSERVATIONS ON MOUNT
WHITNEY
By A. K. Angstrom and E. H. Kennard
In the summer of 1913 an expedition supported by a grant from the
Smithsonian Institution proceeded to California in order to study the noc-
turnal radiation under different atmospheric conditions. In connection with
these investigations we had an opportunity to measure the intensity of the
solar radiation during seven clear days on the summit of Mount Whitney
(4,420 m.). These measurements were made for different air masses and
include observations of the total radiation and of the radiation in a special
part of the spectrum, selected by means of an absorbing screen, as had been
proposed by K. Angstrom.2 Our paper will present the results of the observa-
tions and a computation from them of the solar constant.
INSTRUMENTS
The observations were made with Angstrom's pyrheliometer No. 158. With
this instrument the energy of the radiation falling upon the exposed strip is
given in calories per square centimeter per minute by the relation I = kC2,
where C is the compensating current sent through the shadowed strip, and k is
a constant which was determined for this instrument at the solar observatory
of the Physical Institute in Upsala and found to be 13. 58.3 The compensating
current was furnished by four dry cells, which proved entirely suited to the
purpose. It was measured by a Siemens and Halske milliammeter. For
further details of the instrument and the method of using it, we refer to the
original paper.4
The absorbing screen, used in order to study a limited part of the spectrum,
was composed of a water cell, in which the water layer had a thickness of
1 cm., and a colored glass plate, Schott and Genossen, 436111, the thickness of
which was 2.53 mm. The transmission of the combination for different wave
lengths as previously determined at Upsala by Mr. A. K. Angstrom is given
in figure 16. The maximum of transmission. occurs at wave length 0.526 u.,
and 85 per cent of the transmitted light is included between 0.484 u. and 0.570 \i.
1 Reprinted by permission from the Astrophysical Journal, Vol. 39, No. 4,
PP- 3SO-360.
2 Nova Acta Reg. Soc, Sc. Upsal., Ser. IV, 1, No. 7.
3 A comparison made at the Smithsonian Institution in Washington showed
that the readings of this instrument are 4.57 per cent lower than the Smith-
sonian scale.
4 Astrophysical Journal, 9, 332, 1899.
ISO
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
151
The local time of each observation, from which the sun's zenith angle and
finally the corresponding air mass was computed, was determined from the
readings of three watches. Before and after the expedition to Mount Whit-
ney, the watches were compared with the daily telegraphic time signal at
Claremont, Cal. The time is probably accurate within half a minute.
%
30
10
•45
Fig. 16.-
.50 .55 .60
-Transmission curve of absorbing screen.
• 6S A
The results are given in tables 17 and 18. Table 17 refers to the measure-
ments of the total radiation and contains : (1) the date, (2) the local apparent
time CO, (3) the computed air mass (w), (4) readings of the milliammeter
(s), (5) the total radiation computed from the readings. Table 18 contains the
same quantities relating to measurements taken with the absorbing screen.
Bemporad's1 expression for the air mass in terms of the apparent zenith
angle was employed. His values for 6o°, 70°, 8o°, and 85° were available in
a short table given by F. Lindholm.2 The differences between these values
and the secant of the angle give the (negative) corrections to be applied to
the secants of these angles. Through these values of the correction an alge-
braic curve of four terms was passed and the correction was then calculated
for other angles. In obtaining the apparent zenith angle, allowance was made
for refraction.
1 Mitteilungen der Grossherzoglichen Sternwarte zu Heidelberg, No. 4, 1904.
2 Nova Acta Reg. Soc, Sc. Upsal., Ser. IV, 3, No. 6.
152
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table 17
— Measurements of total radiation
s Q
m
t
VI
Milliamp. _c_
ll.
x£ cm.1
min.
h. m.
August 2
6 34-2
6 49.2
3-337 100. 1 1
2.872 102.5 1
224
287
7 30.7
2.088 106.3 1
38l
8 13.2
1.657
108.8 I
446
9 20.7
1.299
ill. 3 1
5M
August 4
6 28.3
6 ^8.8
3.630
2.672
99-4 1
104.0 1
202
322
7 ~6.8
2.501
104. 1 1
325
8 4-3
1. 741
108.6 1
441
9 6.8
1-359
no. 5 1
493
11 0.3
1 . 089 1 1 1 . 7 1
520
11 8.8
1. 081 1 12.0 1
533
AugUSt 5, A. M
6 29.5
7 2.0
3 . 608 r>7 8
169
296
2.616
103.0 1
7 48.0
I.906
107.0 1
399
8 59-0
1-397
no. 6 1
495
10 0.5
1. 190
in. 1 1
508
August 5, p. m
2 0.3
3 3-3
1 -193
1. 410
in .2 1
5ii
465
109.5 1
4 4-3
1.830
106.3 1
38i
4 33-8
2.185
104.2 1
326
5 4-8
2.783
100. 1 1
224
S 24.3
3-377
96.6 1
141
August 10
6 33-0
7 3-0
3-630
2.681
95.6 1
100.5 1
117
235
7 56.5
1-857
105.5 1
360
August 11
6 27.1
6 54.6
3-952
2.914
96.9 1
101.9 1
147
269
7 40.1
2-053
106.0 1
373
8 41.6
1. 514
109.3 1
460
10 13. 1
1 -177
in. 7 1
525
August 12
6 26.6
4.018
2.817
98.1 1
103.6 1
176
312
6 59-1
7 55-1
1.889
108.5 1
439
8 57-1
1-435
in. 1 1
509
10 43.6
1. 127
113-0 1
56i
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
153
Table 18. — Measurements with absorbing screen
j
Q,n
t
w
Milliamp.
X2
cal.
cm.2min.
h. m.
August 2
6 18.2
4.044
2.733
104.5
II4. I
0.0371
O.0442
6 54-7
7 25.7
2.158
122.0
0.0505
8 22.7
1.589
125-4
0.0534
8 31-7
1-530
126.8
O.0546
9 15-2
I-3I9
128.8
0 . 0562
August 4
6 16.8
4.204
3-3i6
103. 1
112. 1
O.O361
0 . 0426
6 36.3
7 11. 8
2.406
118. 9
0 . 0480
8 9-3
1.699
125-3
0 . 0533
9 19-3
1. 311
128.0
0.0556
11 13-3
1.077
129.9
0.0573
August 5 A.M
6 17.0
4-237
3-352
101.8
0.0352
0 . 0402
6 36 0
108.8
8 3-5
1-755
123. 1
0.0515
9 5-5
1.368
127.9
0.0554
10 7.0
I-I75
129.4
0 . 0568
2 6.8
1.209
1-457
129.3
126.7
0.0567
0.0545
3 12.8
4 11. 8
1.907
122.4
0.0509
4 40.3
2.287
118. 3
0.0475
5 10.3
2.928
114. 1
0.0441
5 30-3
3-6i5
106.6
0 . 0386
August 9
6 14.4
6 33-9
4.607
3-559
96.0
103.4
0.0313
0.0363
11 38.9
1. 126
128.8
0.0563
August 10
6 21.5
4. 211
3.428
100.6
0.0344
0.0387
6 38.0
106.7
7 8.0
2.570
113. 8
0.0439
8 2.0
1.804
122.4
0 . 0508
8 6.0
1.767
122.0
0.0505
August 11
6 14.6
6 33-6
4.716
3.641
102.5
0.0356
0.0395
107.9
7 0.1
2.770
114. 6
0.0445
7 45-i
1.992
122. 1
0.0507
8 si. 1
1.462
127. 1
0.0549
10 18.6
1. 166
129.9
0.0573
August 12
6 13-1
6 34-i
4-895
3.656
99.1
108.0
0.0333
0.0397
7 5-1
2.671
116. 4
0.0459
8 3.6
1.804
123.5
0.0517
9 2.6
1.409
128. 1
0.0557
10 52.6
1. US
I3I-5
0.0587
154 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
GENERAL DISCUSSION OF THE EMPIRICAL METHODS FOR COMPUTING THE SOLAR
CONSTANT
Empirical methods for determining the solar constant from pyrheliometric
measurements alone have been proposed by K. Angstrom1 and by Fowle.1
Both these methods are based upon results obtained from spectrobolometric
observations. Angstrom's method assumes that from Abbot and Fowle's
observations we know both the distribution of energy in the sun's spectrum
and the general transmission of the atmosphere for all wave lengths in terms
of its value for any given wave length. It assumes further that the absorption
caused by the water vapor is a known function of the water-vapor pressure at
the earth's surface; for this, Angstrom proposed an empirical formula based
upon his spectrobolometric curves. The influence of diffusion and absorption
can then be calculated if the transmission for some chosen wave length is
known from pyrheliometric observations on a limited part of the spectrum.
Fowle's method is much briefer. He plots the logarithms of the observa-
tions against the air masses and extrapolates to air-mass zero by means of
the straight line that best fits the points. To the " apparent solar constant "
thus obtained he applies an empirical correction depending upon the locality,
and derived from local spectrobolometric observations.
Since these methods are founded upon the spectrobolometric method, one
may ask, what is the justification for using them instead of the latter? Can
they be expected to give something more than the method upon which they
are founded? To the first question one may reply that the justification lies in
their simplicity, which makes it possible to apply them under a wide range of
conditions where the more cumbersome bolometric method could never be used.
A spectrobolometric investigation, like that of Abbot on Mount Whitney in
1910, will probably always be a rare event. But especially in regard to the
question of solar variability it is desirable that the number of simultaneous
observations be large and extended to as high altitudes as possible.
The second question, whether the abridged methods can ever deserve the
same confidence, or even in rare cases give greater accuracy than the spectro-
bolometric observations, is one that must be answered rather through experi-
mental results than through general considerations. Here, however, two
points may be noted.
The first is, that the spectrobolometric method, which under ideal conditions
is naturally superior to any abridged method, is in all practical cases a method
involving a large number of precautions, some of which are very difficult to
take. The abridged methods, founded as they are upon mean values, may
possibly under special conditions avoid accidental errors to which single
spectrobolometric series are subjected.
Secondly, it may be noted, that even in the analytical method of bolometry,
there arises some uncertainty in regard to the ordinates of the bolometric
curve, corrected for absorption, at the points where absorption bands are
situated. "This causes an uncertainty in the water-vapor correction in this
method as well as in the abridged methods founded upon it.
xNova Acta Reg. Soc, Sc. Upsal., Ser. IV, 1, No. 7.
3 Annals of the Astrophysical Observatory, Smithsonian Inst., 2, 114.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 1 55
The methods just discussed lead to a numerical value for the solar constant.
But the measurements in a selected part of the spectrum lead also to a direct
test of solar variability, which seems likely to be especially valuable because
these observations are not affected by aqueous absorption.
MEASUREMENTS WITH ABSORBING SCREEN
We may put :
I=I0e-y™
where h is the energy transmitted through the absorbing screen at the limit
of the atmosphere, / is its value after passing through the air mass m, and
Y is a constant dependent upon the scattering power of the atmosphere. If
now we plot log / against m, the points should lie on a straight line, whose
ordinate for m = o is log To.
The values of h thus obtained from our observations are given under the
heading h in table 19. The straight lines were run by the method of least
squares, not so much because the presuppositions of this method seemed here
to be satisfied, as because thereby all personal bias was eliminated. The
" probable error " e of each value of h is appended as a rough indication of its
reliability, and the weighted mean h is given at the bottom of the table. A
comparison between the different values of I» shows that they all differ by
less than 2 per cent; half of them by less than Yz per cent from the mean
value. The deviation falls as a rule within the limits of the probable error.
This result thus fails to support the variability of the sun inferred by Abbot
from simultaneous observations at Bassour and iMount Wilson. We cannot,
however, with entire safety draw any conclusions about the total radiation
from measurements in a limited part of the spectrum. All that can be said
with certainty is that a change of the energy in the green part of the solar
spectrum exceeding 2 per cent during the period of our observations is
improbable.
If we, from this, are inclined to infer that the total solar radiation during the
same period was constant, this inclination rests upon a statement by Abbot1
himself to this effect : " So far as the observations 2 may be trusted, then,
they show that a decrease of the sun's emission of radiation reduces the
intensity of all wave lengths ; but the fractional decrease is much more rapid
for short wave lengths than for long."
Yet unpublished measurements by Mr. A. K. Angstrom, in Algeria at 1,160 m.
altitude, give a mean value for h equal to 0.0708, which is in close agreement
with the value 0.0702 given above. On the former occasion Mr. Abbot's
spectrobolometric observations gave a mean value for the solar constant of
1.945. If we assume the energy transmitted by our green glass on Mount
Whitney to bear the same ratio to the total energy, the Mount Whitney
observations give a value for the solar constant reduced to mean solar distance
equal to 1.929, which differs by less than 1 per cent from the former value.
1 Annals of the Astrophysical Observatory, Smithsonian Institution, 3, 133.
1013.
2 Observations of Bassour and Mount Wilson, 1911-1912.
I56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
MEASUREMENTS OF THE TOTAL RADIATION
The general basis of the Angstrom-Kimball method of calculation has
already been described. It is here convenient to make use of the spectrum of
constant energy introduced by Langley, where the abscissa represents the
energy included between an extreme (ultra-violet) wave length and the wave
length corresponding to the abscissa ; the energy-density plotted as ordinate
would then be constant. A table giving wave lengths and corresponding
abscissa; is given by Kimball.1
Referred to such a spectrum, the atmospheric transmission yx for any wave-
length is well represented by the empirical formula
yx—pm§xnm<l>($) (i)
where x is the abscissa, m the air mass, and 8 a quantity dependent upon the
scattering power of the atmosphere. Angstrom made the natural assumption
0(5) =8. Kimball2 finds that 0(8) = V 8 better fits the observations at
Washington and Mount Wilson. In the latter case we have,
/> = o.93, m = o.i8
Making these substitutions in (1) and integrating,
Qm=Qo\ o.g3»lSx°-^m^sdx
Q-93
md
Qm = Qo i -j- 0.18m V 8
Kimball then adds an empirical correction for the absorption due to water
vapor, based upon bolometric measurements at Washington and at Mount
Wilson, and finally obtains
n Qm t„\
(Jo — s (2)
0 Q3«'0
— ; — L 0 r? — [0.061 — o. oo85+o. oi2Eam]
1 -+- o.i07« V 8
where £0 represents the depth in millimeters to which the earth's surface
would be covered by water if all the aqueous vapor were precipitated. We
have adopted this expression, but instead of attempting to determine Eo from
humidity measurements at the earth's surface we have eliminated it betzveen
two equations such as (2) involving different air masses.
Kimball eliminates 8 between two such equations. We have, however,
followed the original method of K. Angstrom and have determined 8 for each
day from our measurements with the green glass. The energy maximum of
the light transmitted by it lies at 0.526 u. (see fig. 1), to which corresponds the
abscissa 0.27 in the constant energy spectrum. Hence for the transmitted
green light
lm=IoO . 93»'sO . 27°-ls'»v'5
from which 8 can be computed. The values of 8 thus obtained are given in
table 19.
1 Bulletin of the Mount Weather Observatory, 1, Parts 2 and 4.
2 Ibid.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
157
In order to compute Qo, a smooth curve was drawn through the observations
and values of Qm for m = 1, 2, and 3 were read off from the curve. These
values and the value of o for the day were inserted in (2) and £0 then elimi-
nated between the first and second and the first and third of the equations thus
obtained. The results are given in table 19 under the headings Q12, Qn\ the
mean of these for each day is given under Qka and represents the solar con-
stant as obtained for that day by the Angstrom-Kimball method.
The mean value of all the measurements, reduced to mean solar distance, is
1.931 — ca (Angstrom scale) or 2.019 (Smithsonian scale). The maximum
cm.2 min.
deviation from the mean is 3 per cent.
Table 19. — Final results
P
mm.
8
cal.
e
per
cent
012
cal.
Qu
cal.
Qka
cal.
Qf
cal.
cm.2min.
cm.2min.
cm.2min.
cm. -mm.
cm.2min.
August
August
August
August
August
August
August
August
2
4
5- A.M.
5- P.M.
9
(3-0?)
3-0
2.5
2.9
O.30
O.28
O.32
O.32
(0-39)
0.33
O.30
O.29
0 . 0689
0 . 0678
0 . 0683
0 . 0684
(0 0688)
0 . 0670
0 . 0685
0 . 0685
0.9
0.9
0-3
0.8
I.904
1.847
1. 871
I.887
1.886
1.829
1.874
1.900
1.895
I-838
1.873
I.894
(1.820)
1-793
1.832
1.878
10
12
3-4
2.2
2.0
0.7
o.S
0.5
1.877
I.896
1.826
1.870
1.888
(I.826)
1.874
I.892
(l.77o)
1-793
1.802
Finally, Fowle's abridged method was applied to the same observations.
Sufficient observations are not available for the elaboration of a special cor-
rection suited to Mount Whitney. But from the values of 5, it appears that
the transmission over Mount Whitney was about the same as over Mount
Wilson, where the average value of 5 is 0.25 ; and the water-vapor pressure,
the most uncertain factor, was low (2-4 mm.). Hence it may not be devoid
of interest to apply here Fowle's rule as elaborated for Mount Wilson, which
is : To the " apparent solar constant " obtained by straight-line extrapolation
add 2.7 per cent and as many per cent as there are millimeters in the water-
vapor pressure. The results thus obtained are given in table 19 under the
heading Qp\ the mean water-vapor pressure is given under p.
cal.
cm/ mm.
cal.
Weighted mean 70 = 0.0683
reduced to mean solar distance h== 00702
cm.- mm.
(Angstrom scale)
Mean reduced to mean solar distance: Qka = 1.931 (A.),
= 2.019 (Sm.)
cal.
cm.- mm.
QF = 1.872 (A.),
= 1.960 (Sm.)
cal.
cm.- mm.
158 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
SUMMARY
Our pyrheliometric observations on the top of Mount Whitney, extending
from August 2 to August 12, 1913, have led to the following results :
1. A variation in the solar constant amounting to more than 2 per cent during
this time is improbable.
2. The solar constant computed from the measurements in a selected part
of the spectrum, reduced to mean solar distance, came out 1.929 — , ' .
cm." min.
(Smithsonian scale), with a possible error of 1.5 per cent. This value is
obtained on the assumption that the energy included between 0.484 u. and
0.576 u is a constant known fraction of the total energy in the solar spectrum.
3. The solar constant computed by the Angstrom-Kimball method was found
to be 2.019 — -f ' . (Smithsonian),
cm. mm.
4. The solar constant computed according to Fowle's method comes out
1.960 — 5-^— (Smithsonian),
cm. min.
The value of the solar constant given in (2) is in close agreement with
Abbot's mean value of 1.932 obtained from several series of observations
made during the years 1902-1912 at much lower altitudes (<?. g., at 1160 m. in
Algeria). The value given in (3) is also in close agreement with the solar
constant computed by Kimball according to the same method from measure-
ments at Washington. Consequently our observations give no support to a
value of the solar constant greatly exceeding 2 — t— '- — .
cm." min.
Because of their bearing upon the question of solar variability, it seems
desirable that the observations in selected parts of the spectrum by means of
absorbing screens should be extended to different localities, and that if possible
simultaneous measurements at elevated stations should be undertaken.
Cornell University,
December, 1913.
Note. — After the publication of the paper treating the pyrheliometric
observations on Mt. Whitney by Dr. Kennard and myself, the spectrobolo-
metric observations at Mt. Wilson have been published by Dr. Abbot. From
both the simultaneous series, it is evident that our observations have been
carried out during a period of relatively high constancy of the solar activity.
No evidence in regard to the variability of the solar radiation can therefore
with safety be drawn from these few observations alone. If the doubtful
observations of August 8 and August 10 are excluded, the simultaneous
observations at the two places seem, however, to confirm one another very
well, as may be seen from figure 17. It seems, therefore, to be probable that
the variations in the computed solar constant values are due to a real solar
variability, the existence of which is very strongly indicated by the work of
several expeditions of the Smithsonian Institution.1
Anders Angstrom.
1 Annals II and III of the Astrophysical Observatory of the Smithsonian
Institution.
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM I 59
&00
1S
1°
US
(
^c
)
I
\
*
\
'/,
1
\
\
\
/
V
\
\
Y
\ N
\
\
\
.AwgwsC )<\\l ,0
Circles : Mt. Wilson solar constant values.
Crosses : Mt. Whitney solar constant values.
Fig. 17.
L
n*
1(?
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